Question

question
complete the square to re - write the quadratic function in vertex form:
(y = 3x^{2}-24x + 49)
answer attempt 1 out of 2(y=) submit answer

Explanation:

Step1: Factor out the coefficient of \(x^2\) from the first two terms

We have \(y = 3x^2 - 24x + 49\). Factor out 3 from the first two terms:
\(y = 3(x^2 - 8x) + 49\)

Step2: Complete the square inside the parentheses

To complete the square for \(x^2 - 8x\), we take half of the coefficient of \(x\) (which is \(-8\)), square it, and add and subtract it inside the parentheses. Half of \(-8\) is \(-4\), and \((-4)^2 = 16\). So we add and subtract 16 inside the parentheses:
\(y = 3((x^2 - 8x + 16) - 16) + 49\)

Step3: Simplify the expression

First, simplify the expression inside the parentheses. \(x^2 - 8x + 16\) is a perfect square, \((x - 4)^2\). Then we distribute the 3:
\(y = 3(x - 4)^2 - 3\times16 + 49\)
Calculate \(-3\times16 = -48\), then:
\(y = 3(x - 4)^2 - 48 + 49\)
Simplify \(-48 + 49 = 1\):
\(y = 3(x - 4)^2 + 1\)

Answer:

\(y = 3(x - 4)^2 + 1\)