Question

5
select the correct answer.
which of these is the standard form of the following function?
$f(x) = 7(x - 1)^2 + 3$
a. $f(x) = 7x^2 - 14x - 10$
b. $f(x) = 7x^2 - 14x + 10$
c. $f(x) = -7x^2 - 14x - 10$
d. $f(x) = -7x^2 - 14x + 10$

Explanation:

Step1: Expand \((x - 1)^2\)

Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = x\) and \(b = 1\), we get \((x - 1)^2 = x^2 - 2x + 1\).

Step2: Multiply by 7

Multiply the expanded form by 7: \(7(x^2 - 2x + 1)=7x^2 - 14x + 7\).

Step3: Add 3

Add 3 to the result: \(7x^2 - 14x + 7 + 3 = 7x^2 - 14x + 10\).

Answer:

B. \(f(x) = 7x^2 - 14x + 10\)