Find the equation of the axis of symmetry for the parabola y = x^2 + x − 6 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify Coefficients: Identify the coefficients of the quadratic equation. The quadratic equation is given by y = ax^2 + bx + c. For the parabola y = x^2 + x − 6, we can compare it to the standard form and identify the coefficients as follows: a = 1 (coefficient of x^2) b = 1 (coefficient of x) c = -6 (constant term)Use Axis of Symmetry Formula: Use the formula for the axis of symmetry. The axis of symmetry for a parabola given by the equation y = ax^2 + bx + c is x = -b/(2a). We will substitute the values of a and b that we found in Step 1 into this formula.Calculate Axis of Symmetry: Calculate the axis of symmetry. Substitute a = 1 and b = 1 into the formula x = -b/(2a): x = -1/(2 * 1) x = -1/2 The axis of symmetry is the vertical line x = -1/2.

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Find the equation of the axis of symmetry for the parabola $y = x^2 + x - 6$ . $\newline$ 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 - 6

\newline

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

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\_\_

Identify Coefficients: Identify the coefficients of the quadratic equation. $\newline$ The quadratic equation is given by $y = ax^2 + bx + c$ . For the parabola $y = x^2 + x − 6$ , we can compare it to the standard form and identify the coefficients as follows: $\newline$ $a = 1$ (coefficient of $x^2$ ) $\newline$ $b = 1$ (coefficient of $x$ ) $\newline$ $c = -6$ (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 $b$ that we found in Step $1$ into this formula.
Calculate Axis of Symmetry: Calculate the axis of symmetry. $\newline$ Substitute $a = 1$ and $b = 1$ into the formula $x = -\frac{b}{2a}$ : $\newline$ $x = -\frac{1}{2 \times 1}$ $\newline$ $x = -\frac{1}{2}$ $\newline$ The axis of symmetry is the vertical line $x = -\frac{1}{2}$ .