Question

SOMEONE PLEASE HELP, I DO NOT UNDERSTAND.

What is the quadratic function that is created with roots -10 and -6 and a vertex at (-8, -8)?

What is the quadratic function that is created with roots at 2 and 4 and a vertex at (3, 1)?

I've actually been trying to figure this out for days, but every time I think I have the right answer and understand how to form the quadratic function, I double check it on a calculator and it doesn't make sense. Could someone please help me out and explain this to me?

Answer 1

to find an equation with specific roots, we have an equation if the form y=A(x-h)(x-k) where the roots are h and k. this is because when you plug in x=h or x=k, you get y=A(h-h)(h-k)=A(0)(h-k) = 0

so for the first question, we have
y=A(x-(-10))(x-(-6))=A(x+10)(x+6)

but the vertex must be at (-8,-8), which means when x=-8, then y=-8

plugging this in we get:
-8=A(-8+10)(-8+6)
-8=A(2)(-2)
-8=A(-4)
A=2

so our final answer is
y=2(x+10)(x+6)

using the same method the answer so the second one is:

y=-(x-2)(x-4)