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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an
(x,y) point.

y=x^(2)-6
Answer:

Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an $(x, y)$ point. $\newline$ $y=x^{2}-6$ $\newline$ Answer:

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Solve exponential equations by rewriting the base

Full solution

Q. Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

point.

\newline

y=x^{2}-6

\newline

Answer:

Identify Vertex: The vertex form of a parabola is given by $y = a(x-h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. To find the vertex of the parabola $y = x^2 - 6$ , we need to identify the values of $h$ and $k$ in this equation.
Determine Coefficients: In the given equation $y = x^2 - 6$ , the coefficient $a$ is $1$ (since there is no coefficient written, it is understood to be $1$ ), and there is no $(x-h)$ term, which means $h = 0$ . The constant term is $-6$ , which means $k = -6$ . Therefore, the vertex of the parabola is at the point $(h, k) = (0, -6)$ .
Conclude Vertex: Since we have identified the vertex without needing to complete the square or use any graphing technology, we can conclude that the vertex of the parabola $y = x^2 - 6$ is at the point $(0, -6)$ .

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