Question

question
find the equation of the axis of symmetry of the following parabola algebraically.
( y = -x^2 + 1 )

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 \( x = -\frac{b}{2a} \).

For the given equation \( y = -x^2 + 1 \), we can identify \( a = -1 \), \( b = 0 \), and \( c = 1 \).

Step2: Substitute the values of \( a \) and \( b \) into the formula for the axis of symmetry.

Substituting \( a = -1 \) and \( b = 0 \) into \( x = -\frac{b}{2a} \), we get \( x = -\frac{0}{2(-1)} \).
Simplifying the right - hand side, \( -\frac{0}{-2}=0 \).

Answer:

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