"Determine an equation of a quadratic function with x-intercepts of 2 and 6, that passes through the point (3, 12)"

Question

anonymous · Answer

I know how to do this question if I'm given the points of the vertex.. but in this case, it isn't. so..

anonymous · Answer

start with 
$$f(x)=a(x-2)(x-6)$$ and then solve for $a$ via $$f(3)=a(3-2)(3-6)=12$$

anonymous · Answer

you get $$a\times 1\times -3=12$$
$$-3a=12$$
$$a=-4$$ so your quadratic is 
$$-4(x-2)(x-6)$$ multiply out if you want

anonymous · Answer

i get $f(x)=-4 x^2+32 x-48$ but check my algebra

anonymous · Answer

@satellite73, I got the same thing but the answer says it should be y =  - 4 ( x - 4 )^2 + 16.

anonymous · Answer

fine. i guess they wanted it in "vertex" form

anonymous · Answer

Oh yeah, nevermind i got it. thank you so much!

anonymous · Answer

convince  yourself that they are equal

anonymous · Answer

yw