SOLUTION: 1) Write the quadratic function rule that has a vertex at (-2,5) and is stretched by a factor of 2 and reflected across the x axis. 2) The vertex of a quadratic function is (1,-

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 1) Write the quadratic function rule that has a vertex at (-2,5) and is stretched by a factor of 2 and reflected across the x axis. 2) The vertex of a quadratic function is (1,-      Log On


   

Question 1131679: 1) Write the quadratic function rule that has a vertex at (-2,5) and is stretched by a factor of 2 and reflected across the x axis.
2) The vertex of a quadratic function is (1,-50). F(5) = -18. Find the function rule, find the roots, and find the y intercept.
3) The roots of a quadratic function are -3 and 7. The quadratic coefficient is -1/5. write the rule in factored form and find the maximum of the function
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


1) vertex at (-2,5); stretched by a factor of 2 and reflected across the x axis

y+=+a%28x%2B2%29%5E2%2B5

with the stretch by a factor of 2 and a reflection across the x-axis, the coefficient a is -2. So

y+=+-2%28x%2B2%29%5E2%2B5

2) vertex (1,-50); f(5) = -18

y+=+a%28x-1%29%5E2-50

find the value of the coefficient a using the (x,y) coordinates of the given point, (5,-18).

-18+=+a%285-1%29%5E2-50
-18+=+16a-50
32+=+16a
a+=+2

y+=+2%28x-1%29%5E2-50

roots: set y = 0 and solve.

0+=+2%28x-1%29%5E2-50
2%28x-1%29%5E2+=+50
%28x-1%29%5E2+=+25
x-1+=+5 or x-1+=+-5
x+=+6 or x+=+-4

The roots are 6 and -4.

y-intercept: set x=0 and evaluate.

y+=+2%280-1%29%5E2-50
y+=+2-50+=+-48

The y-intercept is -48, or (0,-48).

3) roots -3 and 7; coefficient a is -1/5

This one is nearly done for you:

y+=+%28-1%2F5%29%28x%2B3%29%28x-7%29

maximum value: by the symmetry of a parabola, the maximum value is at the x value halfway between the roots, at x=2.

y+=+%28-1%2F5%29%282%2B3%29%282-7%29+=+%28-1%29%28-5%29+=+5

The maximum value is 5.