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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)+4x-2
Answer:

Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an $(x, y)$ point. $\newline$ $y=x^{2}+4 x-2$ $\newline$ Answer:

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Write equations of circles in standard form using properties

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}+4 x-2

\newline

Answer:

Calculate x-coordinate: To find the vertex of the parabola, we can use the vertex formula for a parabola in the form $y = ax^2 + bx + c$ . The x-coordinate of the vertex is given by $-\frac{b}{2a}$ . $\newline$ In our equation, $a = 1$ and $b = 4$ . $\newline$ Let's calculate the x-coordinate of the vertex. $\newline$ x-coordinate = $-\frac{b}{2a}$ = $-\frac{4}{2\cdot 1}$ = $-\frac{4}{2}$ = $-2$
Find y-coordinate: Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting $x = -2$ into the original equation. $\newline$ $y = (-2)^2 + 4*(-2) - 2$ $\newline$ $y = 4 - 8 - 2$ $\newline$ $y = -6$
Determine vertex point: We have found the $x$ -coordinate and $y$ -coordinate of the vertex. Therefore, the vertex of the parabola is at the point $(-2, -6)$ .

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