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

y=-x^(2)+8x
Answer:

Find the equation of the axis of symmetry of the following parabola using graphing technology. $\newline$ $y=-x^{2}+8 x$ $\newline$ 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=-x^{2}+8 x

\newline

Answer:

Identify Coefficients: The equation of a parabola in the form $y = ax^2 + bx + c$ can have its axis of symmetry found using the formula $x = -\frac{b}{2a}$ . Let's identify the coefficients $a$ and $b$ from the given equation $y = -x^2 + 8x$ .
$a = -1$ (coefficient of $x^2$ )
$b = 8$ (coefficient of $x$ )
Find Axis of Symmetry Formula: Now, we will use the formula $x = -\frac{b}{2a}$ to find the axis of symmetry. $\newline$ Substitute the values of $a$ and $b$ into the formula: $\newline$ $x = -\frac{8}{2 \times -1}$
Substitute Values: Perform the calculation: $\newline$ $x = \frac{-8}{-2}$ $\newline$ $x = 4$
Perform Calculation: The equation of the axis of symmetry is a vertical line passing through the $x$ -coordinate we found. Therefore, the equation of the axis of symmetry is $x = 4$ .

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