Question

find the equation for the axis of symmetry for the function f(x) = x² - 6x + 5. a. x = 3 b. x = 6 c. y = 3 d. x = -3

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 equation of the axis of symmetry is \( x = -\frac{b}{2a} \).

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

In the function \( f(x) = x^2 - 6x + 5 \), we have \( a = 1 \) and \( b = -6 \).

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

Substituting \( a = 1 \) and \( b = -6 \) into \( x = -\frac{b}{2a} \), we get:

$$ x = -\frac{-6}{2 \times 1} = \frac{6}{2} = 3 $$

Answer:

A. \( x = 3 \)