Question

find the equation of the axis of symmetry for the parabola $y = x^2$. simplify any numbers and write them as proper fractions, improper fractions, or integers.

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 parabola \( y = x^2 \), we can rewrite it as \( y = 1x^2 + 0x + 0 \). So, \( a = 1 \), \( b = 0 \), and \( c = 0 \).

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 \( x = -\frac{0}{2\times1} \).
Simplifying the right - hand side, \( -\frac{0}{2}=0 \). So the equation of the axis of symmetry is \( x = 0 \).

Answer:

\( x = 0 \)