Question

which function is equivalent to y = 3(x + 4)² + 5?A) y = 3x² + 21B) y = 3x² + 24x + 63C) y = 3x² + 24x + 53D) y = 3x² + 8x + 21

Answer 1

Given: The function

$y=3(x+4)^2+5$

To Determine: The equivalent function of the given function

Solution:

Step 1: Expand the parenthesis

$\begin{gathered} y=3(x+4)^2+5 \\ (x+4)^2=(x+4)(x+4) \\ (x+4)^2=x(x+4)+4(x+4) \\ (x+4)^2=x^2+4x+4x+16 \\ (x+4)^2=x^2+8x+16 \end{gathered}$

Step 2: Substitute the expanded into the function

$\begin{gathered} y=3(x+4)^2+5 \\ y=3(x^2+8x+16)+5 \\ y=3x^2+24x+48+5 \\ y=3x^2+24x+53 \end{gathered}$

Hence, the equivalent function to the given is y = 3x²+24x+53, OPTION C