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

y=x^(2)-4x-2
Answer:

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

\newline

Answer:

Find Vertex: The equation of the parabola is given by $y = x^2 - 4x - 2$ . To find the axis of symmetry, we need to find the $x$ -coordinate of the vertex of the parabola. The axis of symmetry can be found using the formula $x = -\frac{b}{2a}$ , where $a$ and $b$ are the coefficients from the quadratic equation in the form $y = ax^2 + bx + c$ .
Calculate Coefficients: In our equation, $y = x^2 - 4x - 2$ , the coefficient $a$ is $1$ and the coefficient $b$ is $-4$ . We will substitute these values into the formula to find the $x$ -coordinate of the vertex.
Substitute into Formula: Using the formula $x = -\frac{b}{2a}$ , we substitute $a = 1$ and $b = -4$ to get $x = -\frac{(-4)}{2\cdot 1} = \frac{4}{2} = 2$ .
Determine Axis of Symmetry: The $x$ -coordinate of the vertex is $2$ , which means the axis of symmetry is the vertical line that passes through this $x$ -coordinate. Therefore, the equation of the axis of symmetry is $x = 2$ .

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