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

Identify Coefficients: Identify the coefficients of the quadratic equation. The given parabola is y = x^2 + x. This can be compared to the standard form of a quadratic equation, which is y = ax^2 + bx + c. Here, a = 1, b = 1, and c is not given because it is 0.Use Axis of Symmetry Formula: Use the formula for the axis of symmetry. The axis of symmetry for a parabola given by 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 and b = 1, so the axis of symmetry is x = -1/(2 * 1) = -1/2.Write Equation: Write the equation of the axis of symmetry. The axis of symmetry is a vertical line, so its equation is x = constant. In this case, the constant is -1/2. Therefore, the equation of the axis of symmetry is x = -1/2.

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

\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 given parabola is $y = x^2 + x$ . This can be compared to the standard form of a quadratic equation, which is $y = ax^2 + bx + c$ . Here, $a = 1$ , $b = 1$ , and $c$ is not given because it is $0$ .
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry. $\newline$ The axis of symmetry for a parabola given by $y = ax^2 + bx + c$ 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. $\newline$ $a = 1$ and $b = 1$ , so the axis of symmetry is $x = -\frac{1}{(2 \cdot 1)} = -\frac{1}{2}$ .
Write Equation: Write the equation of the axis of symmetry. $\newline$ The axis of symmetry is a vertical line, so its equation is $x = \text{constant}$ . In this case, the constant is $-\frac{1}{2}$ . Therefore, the equation of the axis of symmetry is $x = -\frac{1}{2}$ .