Question

find the axis of symmetry.
f(x) = x² + 2x - 5
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 \( f(x) = x^2 + 2x - 5 \), we have \( a = 1 \) (the coefficient of \( x^2 \)) and \( b = 2 \) (the coefficient of \( x \)).

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

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

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

Step4: Simplify the expression.

Simplifying \( -\frac{2}{2 \times 1} \), we have:

$$ x = -\frac{2}{2} = -1 $$

Answer:

\( x = -1 \)