Question

select the correct answer.
what is the standard form of this function?
f(x) = (x - 2)² + 6

a. f(x) = x² - 4x + 10
b. f(x) = -x² - 6x + 10
c. f(x) = -x² - 8x + 10
d. f(x) = x² - 8x + 10

Explanation:

Step1: Expand the square term

We know that \((a - b)^2 = a^2 - 2ab + b^2\). For \((x - 2)^2\), here \(a = x\) and \(b = 2\), so \((x - 2)^2=x^{2}-2\times x\times2 + 2^{2}=x^{2}-4x + 4\).

Step2: Add the constant term

The function is \(f(x)=(x - 2)^2+6\). Substitute the expanded form of \((x - 2)^2\) into the function: \(f(x)=x^{2}-4x + 4+6\).

Step3: Simplify the constant terms

Combine the constant terms \(4\) and \(6\): \(4 + 6=10\). So \(f(x)=x^{2}-4x + 10\).

Answer:

A. \(f(x)=x^{2}-4x + 10\)