Question

question 5 of 10
which equation represents the standard form of the equation $y=(x + 3)^2 - 4$?

a. $y = x^2 + 3x + 5$

b. $y = x^2 + 6x - 4$

c. $y = x^2 + 3x - 4$

d. $y = x^2 + 6x + 5$

Explanation:

Step1: Expand the square term

We know that \((a + b)^2 = a^2 + 2ab + b^2\). Here \(a=x\) and \(b = 3\), so \((x + 3)^2=x^{2}+2\times x\times3 + 3^{2}=x^{2}+6x + 9\)

Step2: Substitute back into the original equation

The original equation is \(y=(x + 3)^2-4\). Substituting the expanded form of \((x + 3)^2\) we get \(y=x^{2}+6x + 9-4\)

Step3: Simplify the constant terms

Simplify \(9-4 = 5\), so the equation becomes \(y=x^{2}+6x + 5\)

Answer:

D. \(y = x^{2}+6x + 5\)