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Find the equation of the axis of symmetry for the parabola $y = x^2 - 5x + 9$ . $\newline$ 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 - 5x + 9

.

\newline

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

\newline

\_\_

Identify Coefficients: Identify the coefficients of the quadratic equation. $\newline$ The quadratic equation is given by $y = ax^2 + bx + c$ . For the parabola $y = x^2 − 5x + 9$ , we can compare it to the standard form and identify the coefficients as follows: $\newline$ $a = 1$ (coefficient of $x^2$ ) $\newline$ $b = -5$ (coefficient of $x$ ) $\newline$ $c = 9$ (constant term)
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry. $\newline$ The axis of symmetry for a parabola given by the equation $y = ax^2 + bx + c$ is $x = -\frac{b}{2a}$ . We will substitute the values of $a$ and $b$ into this formula to find the axis of symmetry.
Substitute Values: Substitute the values of $a$ and $b$ into the formula. $\newline$ $a = 1$ $\newline$ $b = -5$ $\newline$ $x = -(-5)/(2\cdot1)$ $\newline$ $x = \frac{5}{2}$ $\newline$ The axis of symmetry is therefore $x = \frac{5}{2}$ .

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