Question

find the equation of the axis of symmetry of the following parabola algebraically

y = x² - 9

Explanation:

Step1: Recall the formula for axis of symmetry

For a parabola in the form \( y = ax^2 + bx + c \), the equation of the axis of symmetry is \( x = -\frac{b}{2a} \).

Step2: Identify a and b from the given equation

In the equation \( y = x^2 - 9 \), we can rewrite it as \( y = 1x^2 + 0x - 9 \). So, \( a = 1 \) and \( b = 0 \).

Step3: Substitute a and b into the formula

Substitute \( a = 1 \) and \( b = 0 \) into \( x = -\frac{b}{2a} \). We get \( x = -\frac{0}{2\times1} \).

Step4: Simplify the expression

Simplifying \( -\frac{0}{2\times1} \) gives \( x = 0 \).

Answer:

The equation of the axis of symmetry is \( x = 0 \)