Question

find the equation of the axis of symmetry of the following parabola algebraically.
y = x² + 8x + 22

Explanation:

Step1: Recall the formula for the axis of symmetry of a parabola in the form \( y = ax^2 + bx + c \)

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

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

For the equation \( y = x^2 + 8x + 22 \), we have \( a = 1 \) (the coefficient of \( x^2 \)) and \( b = 8 \) (the coefficient of \( x \)).

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

Substitute \( a = 1 \) and \( b = 8 \) into \( x = -\frac{b}{2a} \). We get \( x = -\frac{8}{2\times1} \).

Step4: Simplify the expression

Simplify \( -\frac{8}{2\times1} \). First, calculate the denominator: \( 2\times1 = 2 \). Then, divide \( -8 \) by \( 2 \): \( -\frac{8}{2} = -4 \).

Answer:

The equation of the axis of symmetry is \( x = -4 \).