Given the function f(x)= ax^2+bx+c?

a)write down the other x intercept if the vertex is (-3,-4) and one x-intercept is (-5,0).


b) another function h(x) has the same roots as f(x) but has y intercept (0,-20). Find the values of a,b,and c for h(x). Rewrite the equation into turning point form by completing the square.








any help with any of the sections is greatly appreciated!

Given the function f(x)= ax^2+bx+c?
(a)


The axis of the function is vertical. Each x-intercept is therefore at the same horizontal distance from the vertex.





The horizontal distance from (-5,0) to (-3, -4) is 2, and moving 2 units to the right of -3 gives -1. The other x-intercept is:


(-1, 0).





(b)


An equation with roots -1 and - 5 is:


g(x) = (x + 5)(x + 1)


g(x) = x^2 + 6x + 5





At the y-intercept, x = 0, and y = 5.


To make the y intercept 20 requires multiplication by 4, giving:


h(x) = 4g(x)


= 4x^2 + 24x + 20.


= 4(x^2 + 6x) + 20


= 4(x^2 + 6x + 9) + (20 - 36)


= 4(x + 3)^2 - 16.

crab apple