Question

Rewrite the function by completing the square.

Answer 1

Answer:

$g(x) = 4(x - 2)^2 -9$

Step-by-step explanation:

Given

$g(x) = 4x^2 - 16x + 7$

Required

Complete the square

Rewrite so that $x^2$ has 1 coefficient

$g(x) = 4(x^2 - 4x) + 7$

Take half of the coefficient of x

$\frac{4}{2} = 2$

Square the result

$(\frac{4}{2})^2 = 2^2$

$(\frac{4}{2})^2 = 4$

Add and subtract the result in the bracket

$g(x) = 4(x^2 - 4x + 4 - 4) + 7$

Expand the bracket to remove -4

$g(x) = 4(x^2 - 4x + 4) - 16 + 7$

$g(x) = 4(x^2 - 4x + 4) -9$

Expand the bracket

$g(x) = 4(x^2 - 2x -2x+ 4) -9$

Factorize

$g(x) = 4(x(x - 2) -2(x-2)) -9$

Factor out x - 2

$g(x) = 4((x - 2)(x-2)) -9$

Express as square

$g(x) = 4(x - 2)^2 -9$