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Find the equation of the axis of symmetry for the parabola $y = x^2 - 9$ . $\newline$ Simplify any numbers and write them as proper fractions, improper fractions, or integers. $\newline$ _____

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Characteristics of quadratic functions: equations

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Q. Find the equation of the axis of symmetry for the parabola

y = x^2 - 9

.

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

_____

Identify values of $a$ and $b$ : The equation of a parabola in the form $y = ax^2 + bx + c$ has an axis of symmetry given by the formula $x = -\frac{b}{2a}$ . First, we need to identify the values of $a$ and $b$ in the given equation $y = x^2 − 9$ .
Compare with standard form: Comparing $y = x^2 - 9$ with the standard form $y = ax^2 + bx + c$ , we can see that $a = 1$ and $b = 0$ , since there is no $x$ term in the equation $y = x^2 - 9$ . The value of $c$ is $-9$ , but it is not needed to find the axis of symmetry.
Substitute into formula: Now we substitute the values of $a$ and $b$ into the formula for the axis of symmetry: $x = -b/(2a)$ . This gives us $x = -0/(2\times1)$ .
Simplify expression: Simplifying the expression $-\frac{0}{(2\cdot1)}$ gives us $x = \frac{0}{2}$ , which further simplifies to $x = 0$ . Therefore, the axis of symmetry for the parabola $y = x^2 − 9$ is the line $x = 0$ .

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