Find the equation of the axis of symmetry for the parabola y = x^2 + x + 15/2 . 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. For the parabola y = x^2 + x + 15/2, we can identify the coefficients as follows: a = 1 (coefficient of x^2) b = 1 (coefficient of x) c = 15/2 (constant term)Use Axis of Symmetry Formula: Use the formula for the axis of symmetry. The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by the formula x = -b/(2a). We will substitute the values of a and b into this formula to find the axis of symmetry.Substitute Values into Formula: Substitute the values of a and b into the formula. a = 1 b = 1 x = -b/(2a) = -1/(2*1) = -1/2Write 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 -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 $y = x^2 + x + \frac{15}{2}$ . $\newline$ 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 + \frac{15}{2}

\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 $y = ax^2 + bx + c$ . For the parabola $y = x^2 + x + \frac{15}{2}$ , we can identify the coefficients as follows: $\newline$ $a = 1$ (coefficient of $x^2$ ) $\newline$ $b = 1$ (coefficient of $x$ ) $\newline$ $c = \frac{15}{2}$ (constant term)
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry. $\newline$ The axis of symmetry for a parabola in the form $y = ax^2 + bx + c$ is given by the formula $x = -\frac{b}{2a}$ . We will substitute the values of $a$ and $b$ into this formula to find the axis of symmetry.
Substitute Values into Formula: Substitute the values of $a$ and $b$ into the formula. $a = 1$ $b = 1$ $x = -\frac{b}{2a} = -\frac{1}{2\cdot 1} = -\frac{1}{2}$
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 $-\frac{1}{2}$ . Therefore, the equation of the axis of symmetry is $x = -\frac{1}{2}$ .