Question

Write "P (x) = -36x^2 + 900x - 1584" in standard vertex form, help please!

Answer 1

y = a(x – h)2 + k, where (h, k) is the vertex;

in our case, P(x) = a Δ/4a ;

a = -36; b = 900; c = -1584;

b/2a = 900/-72 = -12.5;

Δ = 4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;

P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex;

Answer 2

y = a(x – h)2 + k, where (h, k) is the vertex;

in our case, P(x) = a
`(x + b/2a)^(2) -` Δ/4a ;

a = -36; b = 900; c = -1584;

b/2a = 900/-72 = -12.5;

Δ =
`b^(2) -` 4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;

P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex;