Find the equation of the axis of symmetry for the parabola y = x^2 + 3x . 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 in the form y = ax^2 + bx + c. For the equation y = x^2 + 3x, we can see that a = 1 and b = 3. There is no constant term, so c = 0.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: Substitute the values of a and b into the formula. Substituting a = 1 and b = 3 into the formula x = -b/(2a), we get: x = -3/(2*1) x = -3/2Write 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. From the previous step, we found that constant to be -3/2. Therefore, the equation of the axis of symmetry is: x = -3/2

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Find the equation of the axis of symmetry for the parabola $y = x^2 + 3x$ . $\newline$ 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 + 3x

\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 in the form $y = ax^2 + bx + c$ . For the equation $y = x^2 + 3x$ , we can see that $a = 1$ and $b = 3$ . There is no constant term, so $c = 0$ .
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: Substitute the values of $a$ and $b$ into the formula. $\newline$ Substituting $a = 1$ and $b = 3$ into the formula $x = -b/(2a)$ , we get: $\newline$ $x = -3/(2\cdot1)$ $\newline$ $x = -\frac{3}{2}$
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 $x = \text{constant}$ . From the previous step, we found that constant to be $-\frac{3}{2}$ . Therefore, the equation of the axis of symmetry is: $\newline$ $x = -\frac{3}{2}$