Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 65886: Solve for x: x^2 + 7x + 4 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form.
Solve for x: x^2 - 6x + 9 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form.
Solve for x: x^2 + 4x + 7 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form.
The vertex form of a quadratic function is 3(x - 7)^2 - 4. Find the usual y = ax^2 + bx + c form of the quadratic.
Find the vertex of the parabola y = 3(x+1)^2 - 4. Give your answer by filling in the blanks in the following sentence, where the first blank is the coordinates of the vertex, and the second blank is either the word "highest" or the word "lowest".
The vertex is ______ , and this point is the _________ point on the parabola.
Use the Completing the Square method to find the vertex form of the quadratic function y = x^2 + 7x + 12.
Use the Completing the Square method to find the vertex form of the quadratic function y = 2x^ 2 + 8x + 18.
s(t)=-16t^2+vot+so
In this question, use the information above. You may also use your calculator on this question.
We throw a rock into the air with initial velocity of 50 ft/sec, and initial position of 6 ft. Find how high the rock goes before coming back down. To answer this question, fill in the blanks in the following sentence, where the first blank gives this height, and the second blank gives how many seconds into the flight of the rock it reaches this maximum height.
The rock reaches its highest position of _______ feet above the ground after _______ seconds of flight
A farmer has 500 feet of fencing to use to make a rectangular garden. One side of the garden will be a barn, which requires no fencing. How should the pen be built in order to enclose the largest amount of area possible?
Give your answer by filling in the blanks in the following sentence: The farmer should build the pen ______ feet away from the barn, and ________ feet wide, for an area of _______ square feet
Find the x value or values at which the parabola y = x^2 + 4x + 5 crosses the x-axis. If the parabola does not cross the x-axis, write "It does not cross the x-axis".
Find the x value or values at which the parabola y = x^2 + 5x + 4 crosses the x-axis. If the parabola does not cross the x-axis, write "It does not cross the x-axis".
Give the usual ax^2 + bx + c form of the quadratic function which has a = 1, and has two zeros z = -5 and z = 3
Give the usual ax^2 + bx + c form of the quadratic function which has a = 1, and has two zeros z = 3 + 2i and z' = 3 - 2i.
Click here to see answer by Edwin McCravy(2920)   |
Question 65963: ) It is approximately 480 miles from Los Angeles, California, to San Francisco, California. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.How far have you traveled after 3 hours?How far have you traveled after 4 hours?How far have you traveled after t hours (i.e., write a linear function that expresses the distance traveled, d, as a function of time, t).How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 3 hours?How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 4 hours?How far will you HAVE LEFT to travel to reach San Francisco after you have traveled t hours (i.e., write a linear function that expresses the distance to be traveled to reach San Francisco, s, as a function of time, t).
Click here to see answer by venugopalramana(3286)  |
Question 66047: When working out the rule for a quadratic equation (ax^2+bx+c)from a tables of different values how do you find B? I know that a=half second difference pattern and c=y when x=0. I covered it ages ago and its just gone straight out of my head lol.. Thanks Jocelyn
Click here to see answer by checkley71(8405) |
Question 66052: In most businesses, increasing prices of products can negatively impact the number of customers. A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.
Let the number of riders be a function of the fare charged. Graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), find the slope of the graph, find the price at which there will be no more riders, and the maximum number of riders possible.
The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?
If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?
Thank-you so much!
Click here to see answer by ankor@dixie-net.com(6691)  |
Question 66214: I NEED HELP PLEASE!
Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
What is the function that describes this problem?
The ball will be how high above the ground after 1 second?
How long will it take to hit the ground?
What is the maximum height of the ball?
Click here to see answer by venugopalramana(3286) |
Question 66214: I NEED HELP PLEASE!
Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
What is the function that describes this problem?
The ball will be how high above the ground after 1 second?
How long will it take to hit the ground?
What is the maximum height of the ball?
Click here to see answer by Earlsdon(4898) |
Question 66213: For the function y = x2 - 6x + 8, perform the following tasks:
Put the function in the form y = a(x - h)2 + k.
What is the equation for the line of symmetry for the graph of this function?
Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
In your own words, describe how this graph compares to the graph of y = x2?
Click here to see answer by venugopalramana(3286) |
Question 66260: For the function y = x2 - 6x + 8, perform the following tasks:
a) Put the function in the form y = a(x - h)2 + k.
Answer:
Show work in this space.
b) What is the equation for the line of symmetry for the graph of this function?
Answer:
c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
Show graph here.
Explanation of graphing.
d) Describe how this graph compares to the graph of y = x2?
Answer:
Click here to see answer by funmath(2873) |
Question 66259: I'm having a hard time with this problem. Please help!
Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation. Use the vertex form to find the maximum area.
Answer:
Click here to see answer by checkley71(8405) |
Question 66258: Im having a hard time with this problem. Please help!
Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
Answer:
b) The ball will be how high above the ground after 1 second?
Answer:
c) How long will it take to hit the ground?
Answer:
d) What is the maximum height of the ball?
Answer:
Click here to see answer by Earlsdon(4898) |
Question 66247This question is from textbook 
: Please help me solve this equation. "Find a, b, and c so that the parabola whose equation is y=ax^2+bx+c has its vertex (3,2) and passes through the point (-1,10)". I have tried plugging in the point, but I cannot seem to figure it out. Thank you.This question is from textbook
Click here to see answer by ankor@dixie-net.com(6691) |
Question 66493: Please help me solve this problem.
Toward the end of the principals' meeting for the Drug-Free Community campaign project, a total of 21 handshakes were exchanged. Assuming each principal shakes hands once with the other principals, how many principals were present?
Click here to see answer by josmiceli(3003) |
Question 66492: Please help me answer this question.
A wire 36 m long is cut into two pieces. Each piece is bent to form a rectangle which is 1.0 m longer than it is wide. How long should each piece to be minimize the sum of the areas of the two rectangle?
Click here to see answer by stanbon(26259) |
Question 66575This question is from textbook
: Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation. Use the vertex form to find the maximum area.This question is from textbook
Click here to see answer by venugopalramana(3286) |
Question 66620: I'M HAVING A REALLY HARD TIME TRYING TO FIGURE THIS OUT. PLEASE HELP.
When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )
Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation. In the real world, where might these imaginary numbers be used?
Click here to see answer by stanbon(26259) |
Question 66772: Which statement is true for the quadratic equation 0 = -2x^2 - 9x - 4?
I have gotten to the point of -2x^2 - 9x 4 = 0, but I don't know what to do next. My answers are: A. The product of the roots is 4/9
B. The product of the roots is -2.
C. The sum of the roots is 9/2.
D. The sum of the roots is -9/2
I do know that C is not a correct answer (my teacher told me so). THANKS
Oh, by the way I don't have a textbook pg. because our teacher just gave us the problems on paper.
Click here to see answer by Earlsdon(4898) |
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