please helllp! how to find a quadratic function given the maximum value of 6 when x=-2 and one zero is 1?

Question

anonymous · Answer

you can start by writing it in vertex form as $$f(x)=a(x+2)^2+6$$

anonymous · Answer

then solve for $a$ by setting $f(1)=0$

anonymous · Answer

Why do I set it to zero?

anonymous · Answer

Or how do I know to set it to zero?

jim_thompson5910 · Answer

`one zero is 1` means that f(1) = 0

`one zero is 1` is another way of saying `x = 1 is a root of f(x)` or `x = 1 is an x intercept of f(x)`

anonymous · Answer

$$f(1)=0\
f(1)=a(1+2)^2+6=0$$

anonymous · Answer

i.e. $$9a+6=0$$ solve that one

anonymous · Answer

-2/3

anonymous · Answer

whoaa wait hold the phone
is there a typo in this question?

anonymous · Answer

" find a quadratic function given the minimum value of 6 when x=-2 and one zero is 1?"

anonymous · Answer

maximum...

anonymous · Answer

or does it say maybe "MAXIMUM"?

anonymous · Answer

whew

anonymous · Answer

and yes $$a=-\frac{2}{3}$$