Find the equation of the axis of symmetry for the parabola y = x^2 + 4x + 91/10 . 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 in the form y = ax^2 + bx + c. In this case, y = x^2 + 4x + 91/10, so we can compare it to the standard form and identify the coefficients: a = 1 (coefficient of x^2) b = 4 (coefficient of x) c = 91/10 (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 into this formula to find the axis of symmetry.Substitute Values: Substitute the values of a and b into the formula. a = 1 b = 4 x = -b/(2a) = -4/(2*1) = -4/2 = -2Write Axis of Symmetry Equation: 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. In this case, the constant is -2. Therefore, the equation of the axis of symmetry is x = -2.

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Find the equation of the axis of symmetry for the parabola $y = x^2 + 4x + \frac{91}{10}$ . $\newline$ 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 + 4x + \frac{91}{10}

\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 in the form $y = ax^2 + bx + c$ . In this case, $y = x^2 + 4x + \frac{91}{10}$ , so we can compare it to the standard form and identify the coefficients: $\newline$ $a = 1$ (coefficient of $x^2$ ) $\newline$ $b = 4$ (coefficient of $x$ ) $\newline$ $c = \frac{91}{10}$ (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. $\newline$ $a = 1$ $\newline$ $b = 4$ $\newline$ $x = -\frac{b}{2a} = -\frac{4}{2\cdot 1} = -\frac{4}{2} = -2$
Write Axis of Symmetry Equation: Write the equation of the axis of symmetry. $\newline$ The axis of symmetry is a vertical line, so its equation is of the form $x = \text{constant}$ . In this case, the constant is $-2$ . $\newline$ Therefore, the equation of the axis of symmetry is $x = -2$ .