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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=3x^(2)-12
Answer:

Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an $(x, y)$ point. $\newline$ $y=3 x^{2}-12$ $\newline$ Answer:

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Write a quadratic function from its x-intercepts and another point

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=3 x^{2}-12

\newline

Answer:

Vertex Form Explanation: The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. To find the vertex of the parabola given by $y = 3x^2 - 12$ , we need to complete the square or use the vertex formula $h = -\frac{b}{2a}$ and $k = c - \frac{b^2}{4a}$ for the standard form $y = ax^2 + bx + c$ . In this case, $a = 3$ , $b = 0$ , and $c = -12$ . Since there is no $b$ term, the vertex will be at $(h, k)$ $0$ . To find the $(h, k)$ $1$ -coordinate of the vertex, we substitute $(h, k)$ $2$ into the equation $y = 3x^2 - 12$ .
Calculate Vertex Coordinates: Substitute $x = 0$ into the equation $y = 3x^2 - 12$ to find the $y$ -coordinate of the vertex. $\newline$ $y = 3(0)^2 - 12$ $\newline$ $y = 0 - 12$ $\newline$ $y = -12$ $\newline$ So, the $y$ -coordinate of the vertex is $-12$ .
Final Vertex Coordinates: We have found the x-coordinate of the vertex to be $0$ and the y-coordinate to be $-12$ . Therefore, the coordinates of the vertex of the parabola $y = 3x^2 - 12$ are $(0, -12)$ .

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