SOLUTION: Including: a) ALL X INTERCEPTS ARE CORRECT AND LABELED TO THREE DECIMAL PLACES b) ALL Y INTERCEPTS ARE LABELED c) The COORDINATES OF the MAXIMUM OR MINIMUM value are labeled

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Question 195245: Including:
a) ALL X INTERCEPTS ARE CORRECT AND LABELED TO THREE DECIMAL PLACES
b) ALL Y INTERCEPTS ARE LABELED
c) The COORDINATES OF the MAXIMUM OR MINIMUM value are labeled
d) Graph y= -x^2+4x+1.
Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
PAY NO ATTENTION TO JOHN......WHATS ANNOYING IS SOME ONE WHO TYPES IN LARGE FONTS ALL THE TIME

a) -x%5E2%2B4x%2B1 (-.24,0) and (4.24,0)
:
b)set x equal to zero y=-(0)^2+4(0)+1=1
y intercept is 1: (0,1)
:
c) maximum is y=-1%28x%5E2-4x%2B4%29%2B4%2B1-->y=-1%28x-2%29%5E2%2B5
:
so maximum is (2,5)
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B4x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A-1%2A1=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+20+%29%29%2F2%5C-1+=+-0.23606797749979
x%5B2%5D+=+%28-%284%29-sqrt%28+20+%29%29%2F2%5C-1+=+4.23606797749979

Quadratic expression -1x%5E2%2B4x%2B1 can be factored:
-1x%5E2%2B4x%2B1+=+%28x--0.23606797749979%29%2A%28x-4.23606797749979%29
Again, the answer is: -0.23606797749979, 4.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B4%2Ax%2B1+%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Is there some reason that you feel the need to shout? Typing in all CAPS is the electronic equivalent of shouting and is both rude and annoying.




Use the quadratic formula to determine the roots of



The two x-intercepts will be the points and where and are the roots of the equation.

Substitute 0 for x and do the arithmetic to calculate the value of the y-coordinate of the y-intercept. The y-intercept will be the point where y is the y-coordinate value you just calculated.

The vertex of a parabola whose equation is:



has an x-coordinate equal to . Once you calculate this x-coordinate value, substitute that value for x in the equation and do the arithmetic to calculate the y-coordinate of the vertex.


John