Find the equation of the axis of symmetry for the parabola y = x^2 − x − 8 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify Coefficients: Identify the coefficients a, b, and c in the quadratic equation y = ax^2 + bx + c. The given equation is y = x^2 − x − 8, which can be compared to y = ax^2 + bx + c. Here, a = 1, b = -1, and c = -8.Use Axis of Symmetry Formula: Use the formula for the axis of symmetry, which is x = -b/(2a), to find the axis of symmetry for the given parabola. Substitute the values of a and b into the formula. x = -(-1)/(2*1) x = 1/2Write Equation of Symmetry: Write the equation of the axis of symmetry. The axis of symmetry is a vertical line, so its equation is of the form x = constant. Therefore, the equation of the axis of symmetry for the parabola y = x^2 − x − 8 is x = 1/2.

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Find the equation of the axis of symmetry for the parabola $y = x^2 - x - 8$ . $\newline$ Simplify any numbers and write them as proper fractions, improper fractions, or integers. $\newline$ $\_\_\_\_\_$

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Algebra 2

Characteristics of quadratic functions: equations

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

y = x^2 - x - 8

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

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Identify Coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $y = ax^2 + bx + c$ . The given equation is $y = x^2 - x - 8$ , which can be compared to $y = ax^2 + bx + c$ . Here, $a = 1$ , $b = -1$ , and $c = -8$ .
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry, which is $x = -\frac{b}{2a}$ , to find the axis of symmetry for the given parabola. $\newline$ Substitute the values of $a$ and $b$ into the formula. $\newline$ $x = -\frac{-1}{2\cdot 1}$ $\newline$ $x = \frac{1}{2}$
Write Equation of Symmetry: Write the equation of the axis of symmetry. $\newline$ The axis of symmetry is a vertical line, so its equation is of the form $x = \text{constant}$ . $\newline$ Therefore, the equation of the axis of symmetry for the parabola $y = x^2 − x − 8$ is $x = \frac{1}{2}$ .