Question

write the function in standard form.
$f(x) = 5(x + 3)^2 - 1$
$f(x) = \square$
(simplify your answer. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Expand the square term

We know that \((a + b)^2 = a^2 + 2ab + b^2\). Here \(a=x\) and \(b = 3\), so \((x + 3)^2=x^{2}+6x + 9\).
The function \(f(x)=5(x + 3)^2-1\) becomes \(f(x)=5(x^{2}+6x + 9)-1\).

Step2: Distribute the 5

Multiply each term inside the parentheses by 5: \(5\times x^{2}=5x^{2}\), \(5\times6x = 30x\), \(5\times9=45\). So the function is \(f(x)=5x^{2}+30x + 45-1\).

Step3: Combine like terms

Combine the constant terms \(45-1 = 44\). So the function in standard form is \(f(x)=5x^{2}+30x + 44\).

Answer:

\(f(x)=5x^{2}+30x + 44\)