Question

convert the quadratic equation below from vertex form to standard form. which equation is equivalent?
y = 2(x + 5)^2+11

Explanation:

Step1: Expand \((x + 5)^2\)

Using the formula \((a + b)^2=a^{2}+2ab + b^{2}\), where \(a=x\) and \(b = 5\), we have \((x + 5)^2=x^{2}+10x + 25\).

Step2: Multiply by 2

\(y=2(x^{2}+10x + 25)+11\), then \(y = 2x^{2}+20x+50 + 11\).

Step3: Combine like - terms

\(y=2x^{2}+20x + 61\).

Answer:

\(y = 2x^{2}+20x+61\)