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Find the equation of the axis of symmetry of the following parabola using graphing technology.

y=4x^(2)+24 x+40
Answer:

Find the equation of the axis of symmetry of the following parabola using graphing technology. $\newline$ $y=4 x^{2}+24 x+40$ $\newline$ 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 using graphing technology.

\newline

y=4 x^{2}+24 x+40

\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 $a = 4$ , $b = 24$ , and $c = 40$ .
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry for a parabola in the form $y = ax^2 + bx + c$ . $\newline$ The axis of symmetry can be found using the formula $x = -\frac{b}{2a}$ .
Substitute Values: Substitute the values of $a$ and $b$ into the formula. $x = \frac{-24}{(2\cdot4)}$ $x = \frac{-24}{8}$ $x = -3$
Write Equation of Symmetry: Write the equation of the axis of symmetry. $\newline$ The axis of symmetry is a vertical line, so its equation is $x = \text{constant}$ . $\newline$ Therefore, the equation of the axis of symmetry is $x = -3$ .

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