Write this in Factored and standard form

Question

I have a parabola that is written as f(x)= -(x-12)^2+24 I’m vertex form. Can some show me how to write this in standard and factored form?

Answer 1

y= a(x-h)^2 + k has vertex (h,k)

for f(x) = -(x-12)^2 + 24 where (h,k) = (12,24) = the vertex

it's a downward opening parabola with vertex or maximum point (12,24)

standard form is

y = -(x^2 -24x + 144) + 24

=-x^2 +24x -144 + 24

= -x^2 +24x - 120

y=ax^2 + bx + c where a=-1, b = 24 and c= -120

factored form would be factors of the trinomial, but there are no integer factors

y = -(x^2 -24x + 120)

= -(x--12-2sqr6)(x+12+2sqr6) has irrational factors, because the x intercepts are irrational