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Find the equation of the axis of symmetry of the following parabola algebraically.

y=2x^(2)+24 x+70
Answer:

Find the equation of the axis of symmetry of the following parabola algebraically. $\newline$ $y=2 x^{2}+24 x+70$ $\newline$ Answer:

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Find the axis of symmetry of a parabola

Full solution

Q. Find the equation of the axis of symmetry of the following parabola algebraically.

\newline

y=2 x^{2}+24 x+70

\newline

Answer:

Identify General Form: Identify the general form of the quadratic equation. $\newline$ The given parabola is in the form $y = ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are constants. $\newline$ For the given equation $y = 2x^2 + 24x + 70$ , we have: $\newline$ $a = 2$ , $b = 24$ , and $c = 70$ .
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry for a parabola. $\newline$ The axis of symmetry for a parabola given by $y = ax^2 + bx + c$ is $x = -\frac{b}{2a}$ .
Substitute Values: Substitute the values of $a$ and $b$ into the formula. $\newline$ Substitute $a = 2$ and $b = 24$ into the formula $x = -\frac{b}{2a}$ to find the axis of symmetry. $\newline$ $x = -\frac{24}{2 \times 2}$ $\newline$ $x = -\frac{24}{4}$ $\newline$ $x = -6$
Write Equation: Write the equation of the axis of symmetry. $\newline$ The equation of the axis of symmetry is a vertical line passing through the $x$ -coordinate found in Step $3$ . $\newline$ Therefore, the equation of the axis of symmetry is $x = -6$ .

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