Question

what is the axis of symmetry of h(x) = 5x² + 40x + 64?
○ x = -16
○ x = -4
○ x = 4
○ x = 16

Explanation:

Step1: Recall the formula for axis of symmetry

For a quadratic function in the form \( h(x) = ax^{2}+bx + c \), the axis of symmetry is given by the formula \( x=-\frac{b}{2a} \).

Step2: Identify the values of \( a \) and \( b \)

In the function \( h(x)=5x^{2}+40x + 64 \), we have \( a = 5 \) and \( b=40 \).

Step3: Substitute the values into the formula

Substitute \( a = 5 \) and \( b = 40 \) into the formula \( x=-\frac{b}{2a} \).
We get \( x=-\frac{40}{2\times5} \).

Step4: Simplify the expression

First, calculate the denominator: \( 2\times5 = 10 \).
Then, \( -\frac{40}{10}=- 4 \).

Answer:

\( x = - 4 \) (corresponding to the option "x = -4")