Question

Write p(x) = 21 + 24x + 6x2 in vertex form.

Answer 1

ANSWER

$p(x)=-3+6(x+2)^2$

EXPLANATION

The given function is

$p(x)=21+24x+6x^2$

We make the coefficient of $x^2$ unity by factoring $6$ out of the last two terms to obtain;

$p(x)=21+6(4x+x^2)$

We now add and subtract half the coefficient of $x$ multiplied by a factor of 6 to obtain;

$p(x)=21-6(2)^2+6(2)^2+6(4x+x^2)$

We now factor 6 out of the last two terms to get;

$p(x)=21-6\times 4+6((2)^2+4x+x^2)$

$p(x)=21-24+6((2)^2+4x+x^2)$

The quadratic trinomial in the parenthesis is now a perfect square.

$p(x)=-3+6(x+2)^2$

Hence the vertex form of the polynomial is

$p(x)=6(x+2)^2-3$

Answer 2

Answer:

p(x) = 6(x + 2)2 –3

Hoped I helped!

Step-by-step explanation: