Question Rewrite $f(x)=4(x-1)^{2}-2$ in the form $f(x)=a x^{2}+b x+c$ .

Studdy Solution

STEP 1

Assumptions
1. The given function is $f(x)=4(x-1)^{2}-2$ .
2. We need to rewrite the function in the form $f(x)=ax^{2}+bx+c$ .

STEP 2

Expand the squared term in the function using the formula $(a-b)^2 = a^2 - 2ab + b^2$ .
$f(x) = 4[(x)^2 - 2(x)(1) + (1)^2] - 2$

STEP 3

Distribute the 4 across the terms inside the brackets.
$f(x) = 4(x^2 - 2x + 1) - 2$

STEP 4

Multiply each term inside the brackets by 4.
$f(x) = 4x^2 - 8x + 4 - 2$

STEP 5

Combine the constant terms.
$f(x) = 4x^2 - 8x + 2$

STEP 6

Now the function is in the desired form $f(x)=ax^{2}+bx+c$ where $a=4$ , $b=-8$ , and $c=2$ .
$f(x)=4x^{2}-8x+2$

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