we know that The vertex form for a parabola that opens up or down is:f(x) = a(x - h)^2 + kin the given equation, a=-4, therefore we add zero to the original equation in the form of 4h²−4h² f(x) = –4x² + 24x + 4h²−4h² +13 Factor 4 out of the first 3 terms and group them f(x) = –4*(x² -6x +h²) +4h² +13 We can find the value of h by setting the middle term equal to -2hx −2hx=−6x h=3 and 4h²=36 f(x) = –4*(x² -6x +9) +36 +13
we know that the term (x² -6x +9) is equals to------> (x-3)² so f(x) = –4*(x-3)² +49