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?
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:
