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Question 599194: 2x^2+16x=0 help please
Click here to see answer by MrNumero(1)

Question 599315: How would you write an equation of a quadratic function who's zeros are 6,0
Click here to see answer by jim_thompson5910(28546)

Question 599397: multiply (v+p)(v^2-vp+p^2)

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Question 599427: How do you factor x^2 + 5xy - 14y^2 ?
Click here to see answer by jim_thompson5910(28546)

Question 599183: Ernie Thayer1 hits a baseball and it travels for 409.6 feet before it lands. When he hits the ball, the ball is between about 2 feet and about 5 feet high. If we ignore air resistance, then physics tells us that the flight of the baseball can be modelled using a quadratic equation of the form:

y=ax2 +bx+c, where x is the horizontal distance that the ball has travelled, and y is the height

of the ball at the given distance. Background: To determine the coefficients in a polynomial equation of degree

n:
y=a0xn +a1xn-1 +a2xn-2 +···+an-2x2 +an-1x+an,
one generally to know n + 1 points. With additional information about the poly- nomial, the number of points that are needed can sometimes be reduced. (This additional information is sometimes called symmetry.)

In addition, if we know certain kinds of points, then there may be special forms of the polynomial equation that are easier to work with. For example, if we know that a cubic has its zeros at 1, 2 and 3, then we can use the three x-intercepts form of the cubic to simplify our work – in particular, we know that the cubic has the following form:

y = a(x - 1)(x - 2)(x - 3).
We still need a fourth point on the cubic to determine the value of the constant a.

In this lab, we will focus on 2nd degree or quadratic polynomial equations:
y=ax2 +bx+c.

1. There are many quadratic equations that you could use to model the dis- tance x and the height y, but we want to find one that is realistic. Because of this real-life interaction, not every quadratic equation will be acceptable. Let’s consider some of the properties that an appropriate quadratic equation will have. Answer the following questions:
1.
(a) The following questions deal with the initial height of the ball:
With respect to the real life situation, what is happening when x = 0?

What are the possible values for y when x = 0?
With respect to the graph of the quadratic equation, what is this
point called?
•
(b) The following questions deal with the maximum height of the ball:
What is the name of the point on the graph (a parabola) where the maximum height is attained?

Are some values of y unreasonable?
How is this information important for choosing a window for the
graph?
•
(c) The following questions deal with the ending values for the flight of the ball:

What would be the height of the ball when x = 409.6 feet?

This point on the graph has a name. What is it called?
With respect to the quadratic polynomial, this value of x has a name. What is it called?
•
(d) Using the information collected above, explain why the following equa- tions are poor models of the situation. Give coordinates of points on the graph that support your claim.

i. y = -0.002x(x - 409.6). ii. y = -0.5x2 +216x+3.
iii. y = -0.002x2 + 0.879x + 3.981. iv. y = -0.002x2 + 0.8732x - 3.981.
•
(e) Why is the constant a in the equation y = ax2 +bx+c negative in a reasonable model?

5

Part II. Using given information about the graph to find the quadratic equation.

2. There are different algebraic ways to find a reasonable quadratic model of the situation. We have some information about the path of the ball, giving some information about points of its graph (a parabola).

Suppose the ball was 4.56 feet above ground when Ernie Thayer hit it, and that it reached a maximum height of approximately 108.42 feet when it was approximately 202.6 feet away from where he hit the ball. The ball lands after travelling a ground distance of approximately 409.6 feet.

We will find equations to model the situation by using two algebraic meth- ods. (Show all your work for each part.)

(a) Find an equation of the form y = C(x - z1)(x - z2) where z1 and z2 are the zeros (or roots) of the quadratic polynomial (or x-intercepts of the graph) and C is a scaling constant that needs to be determined.

Find the other root. (Hint: Use the known root, the vertex, and a symmetry property of the graph.)

Find the constant C. (Round this value to three significant posi- tions. Leading zeros are not significant, but trailing zeros are signif- icant. For example, 0.0003478 would be rounded to 0.000348 and 0.0003501 would be rounded to 0.000350. Hint: To find C, you can use the initial height.)

Write out the equation that you found and algebraically check that it satisfies all the necessary conditions. (Note: Show your work! Expect small errors because of rounding.)

(b) Find an equation of the form y = A(x - h)2 + k where the vertex is at (h, k) and the constant A is a scaling factor.

Based on the information that you were given, what are the coordi- nates of the vertex.

Find the constant A. (Round this value to three significant positions.)
Write out the equation that you found and algebraically check that it satisfies all the necessary conditions. (Note: Show your work! Expect small errors because of rounding.)

6

Part III. Discussion of when algebra can be used to find a quadratic equation.
3. In part II, we used two different methods to find a quadratic equation to model the situation. Each required different information about the graph.
1.
(a) Can you use algebra to find a quadratic equation if you know the coor- dinates of just one point on its graph?

2.
(b) Can you use algebra to find a quadratic equation if you know the co- ordinates of just two points on its graph? If so, what information is needed?

3.
(c) Rounding errors in the data might result in your finding different cor- rect equations for your answers in parts (a) and (b) above for Problem 2. What characteristic of the data causes this to happen?
Click here to see answer by richard1234(5390)

Question 599830: Not understanding what I need to compare: question is. Compare the graph of each function:
F(x)=x^2
g(x)=5x^2+10
Click here to see answer by stanbon(57290)

Question 600064: Solve the equation by completing the square. p^2 + 4p + 6 = 0
Click here to see answer by lynnlo(4155)

Question 600103: how do i find the vertex and axis of symmetry for f(x)= -2x^2-4x+2 ?
Click here to see answer by Alan3354(30993)

Question 600154: Solve the equation using the method of square roots.
5b^2-10=0
Click here to see answer by solver91311(16877)

Question 600274: The Robinsons wish to increase the area of their 8-by-6 foot garden by 6 times the current amount. To do this they have decided to add the same amount to each side of the garden. How much should be added to each side of the garden?
Click here to see answer by ankor@dixie-net.com(15647)

Question 600293: find the solution for y=x^2-6x-9
Click here to see answer by richwmiller(9135)

Question 600338: 4x^2+8x+5=0
Click here to see answer by jim_thompson5910(28546)

Question 600338: 4x^2+8x+5=0
Click here to see answer by stanbon(57290)

Question 600305: I need to solve x^2+6x-16=0 by completing the square
Click here to see answer by jim_thompson5910(28546)

Question 600402: apply the quadratic formula to find the roots of the given function, and then graph the function.
0 = x2 - 9
How do I graph this with no y
0 = x2 – 9
Move x to the right side of the equation
X^2-9=0
Add 9 to both sides
X^2=9
Take the square root of both sides to eliminate the exponent
X=+-(sqr)/9
3 is a perfect square
X=+-3
Substitute + for +-
X=3
Substitute - for +-
X=-3

Click here to see answer by mananth(12270)

Question 600398: factor the quadratic expression completely, and find the roots of the expression.
6x^2-17x+2
If possible can you write out each step so I can apply this process in future problems Thanks for all of you help!
Click here to see answer by mananth(12270)

Question 600404: A ball is kicked upward with an initial velocity of 56 feet per second. The ball's height h (in feet) can be expressed as a function of time t (in seconds) by the equation h = -16t2 + 56t. How much time does the ball take to reach its highest point?
Click here to see answer by nerdybill(6958)

Question 600406: factor the quadratic expression completely, and find the roots of the expression.
12x^2 +7x-12
Click here to see answer by w_parminder(53)

Question 600347: What number can be added to both the numerator and the denominator of this fraction to produce the fraction on the right? 19/37 + ? = 4/7
Click here to see answer by alicealc(281)

Question 600462: construct a quadratic equation whose solutions are -5, 7
Click here to see answer by Edwin McCravy(8904)

Question 600556: I Need Help With This Question:
Given the quadratic equation y = 2xSquared + 4x + 5 identify the value of y when x = 0

Click here to see answer by jim_thompson5910(28546)

Question 600633: (x-2y)^3

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Question 600662: Solve by the Quadratic Formula.
3x^2-2x-7=0

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Question 600838: if 3x^2 - 4x + 7 = 0, then (x - 2/3)^2 = ???
Click here to see answer by stanbon(57290)

Question 600838: if 3x^2 - 4x + 7 = 0, then (x - 2/3)^2 = ???
Click here to see answer by mananth(12270)

Question 600848: Factor
5w^2-13w+6
Click here to see answer by Rcmathtutor(12)

Question 600872: complete the square, and find the roots of the quadratic equation.
x2 + 6x -16= 0

Click here to see answer by nerdybill(6958)

Question 600984: The graph of y=-2x^2 + 15x + c contains (3, 89). Find the value of c.
A. 50
B. 62
C. 26
D. none of these
Click here to see answer by lynnlo(4155)

Question 600984: The graph of y=-2x^2 + 15x + c contains (3, 89). Find the value of c.
A. 50
B. 62
C. 26
D. none of these
Click here to see answer by Earlsdon(6287)

Question 600958: Helllllp I don't know how to find a discriminant. u_u
ex: 2x^2+5x+6=0

d=
# of real number solutions:

Also, suppose a parabola has a vertex in Quadrant I and a<0 in the equation y=ax^2+bx+c. How many real solutions will the equation ax^2+bx+c=o have?

Click here to see answer by lawdej(58)

Question 600979: During the first part of a trip, a canoeist travels 45 miles at a certain speed. The canoeist travels 20 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?
The speed on the first part of the trip was _______ mph.
Click here to see answer by ankor@dixie-net.com(15647)

Question 601162: how do you solve a qudratic equation?
Click here to see answer by solver91311(16877)

Question 601192: please help me construct a quadratic equation with the solutions of sqr(3) and sqr(-3)
Click here to see answer by solver91311(16877)

Question 601306: 12x^2-15=0
Click here to see answer by flame8855(424)

Question 601283: apply the quadratic formula to find the roots of the given function, and then graph the function.
0 = x² - 9
Click here to see answer by Edwin McCravy(8904)

Question 601378: (x-3)^2=9
Click here to see answer by w_parminder(53)

Question 601378: (x-3)^2=9
Click here to see answer by lawdej(58)

Question 601401: How do you find all the x-intercepts of the given function:
f(x)=(x2-6x)2-22(x2-6x)-135
the "2"'s are squares
Click here to see answer by ewatrrr(10682)

Question 601432: Solve the Equation.
x-10^x+24=0
Click here to see answer by Alan3354(30993)

Question 601460: 2xsq-12x+10=0
Click here to see answer by jim_thompson5910(28546)

Question 601497: Determine the values of k so that the equation x^2+kx+36=0 will have one real root.please show me step by step.
Click here to see answer by solver91311(16877)

Question 601498: If 2x²-6x=0, then
Click here to see answer by scott8148(6628)

Question 601522: S=3x^2-21x+105 models spending by travelers to a country, in billions of dollars, x years after 2000. what year did travelers spend $75 billion.
Click here to see answer by flame8855(424)

Question 601621: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2+bx+c=0. Solution: 4,only solution.
Thank you
Click here to see answer by stanbon(57290)

Question 601653: factor the quadratic expression completely, and find the roots of the expression.
66x2 - 130x + 56
Click here to see answer by jim_thompson5910(28546)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250