Find the equation of the axis of symmetry for the parabola y = x^2 + 8x + 9 . 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. For the given equation y = x^2 + 8x + 9, we have: a = 1, b = 8, and c = 9.Use Axis of Symmetry Formula: Use the formula for the axis of symmetry of a parabola, which is x = -b/(2a). Substitute the values of a and b into the formula. x = -8/(2 × 1)Simplify Expression: Simplify the expression to find the value of x that represents the axis of symmetry. x = -8/2 x = -4Write Equation of Symmetry: Write the equation of the axis of symmetry using the value of x found in the previous step. 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 is x = -4.

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Find the equation of the axis of symmetry for the parabola $y = x^2 + 8x + 9$ . $\newline$ 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 + 8x + 9

\newline

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

\newline

\_\_

Identify Coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $y = ax^2 + bx + c$ . For the given equation $y = x^2 + 8x + 9$ , we have: $a = 1$ , $b = 8$ , and $c = 9$ .
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry of a parabola, which is $x = -\frac{b}{2a}$ . Substitute the values of $a$ and $b$ into the formula. $x = -\frac{8}{2 \times 1}$
Simplify Expression: Simplify the expression to find the value of $x$ that represents the axis of symmetry. $x = \frac{-8}{2}$ $x = -4$
Write Equation of Symmetry: Write the equation of the axis of symmetry using the value of $x$ found in the previous step. $\newline$ 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 is $x = -4$ .