2x2 + 12x − 2 can be written in the form a(x + b)2 - c. Find the values of a, b and c.

Question

ScanSolve AI Tutor · Accepted Answer

Thanks for the clearer image, 10K! I can read this one now.

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To write $2x^2 + 12x - 2$ in the form $a(x+b)^2 - c$ , we use the method of completing the square.

Factor out the coefficient of $x^2$ from the terms involving $x$ .
$2x^2 + 12x - 2 = 2(x^2 + 6x) - 2$
Complete the square for the expression inside the parenthesis.
Take half of the coefficient of $x$ (which is $6/2 = 3$ ) and square it ( $3^2 = 9$ ). Add and subtract this value inside the parenthesis.
$2(x^2 + 6x + 9 - 9) - 2$
Rewrite the perfect square trinomial.
$2((x+3)^2 - 9) - 2$
Distribute the 2 to both terms inside the parenthesis.
$2(x+3)^2 - 2 \times 9 - 2$ $2(x+3)^2 - 18 - 2$
Combine the constant terms.
$2(x+3)^2 - 20$
Compare this with the given form $a(x+b)^2 - c$ .
By comparing $2(x+3)^2 - 20$ with $a(x+b)^2 - c$ , we can identify the values of $a$ , $b$ , and $c$ .
$a = 2$
$b = 3$
$c = 20$

The values are $a=2, b=3, c=20$ .

2x2 + 12x - 2 can be written in the form a(x + b)2 - c. Find the values of a, b and c.