Question

find the axis of symmetry.
7
f(x) = 2x² - 8x - 1
x =

Explanation:

Step1: Recall the formula for the axis of symmetry of a quadratic function.

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

Step2: Identify the values of \( a \) and \( b \) from the given function.

In the function \( f(x) = 2x^2 - 8x - 1 \), we have \( a = 2 \) and \( b = -8 \).

Step3: Substitute the values of \( a \) and \( b \) into the formula.

Substituting \( a = 2 \) and \( b = -8 \) into \( x = -\frac{b}{2a} \), we get:

$$ x = -\frac{-8}{2 \times 2} $$

Step4: Simplify the expression.

First, simplify the numerator: \( -(-8) = 8 \).
Then, simplify the denominator: \( 2 \times 2 = 4 \).
So, \( x = \frac{8}{4} = 2 \).

Answer:

\( x = 2 \)