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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) (x, y) point.\newliney=x2+4x−2 y=x^{2}+4 x-2 \newlineAnswer:

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Q. Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x,y) (x, y) point.\newliney=x2+4x−2 y=x^{2}+4 x-2 \newlineAnswer:
  1. Calculate x-coordinate: To find the vertex of the parabola, we can use the vertex formula for a parabola in the form y=ax2+bx+cy = ax^2 + bx + c. The x-coordinate of the vertex is given by −b2a-\frac{b}{2a}.\newlineIn our equation, a=1a = 1 and b=4b = 4.\newlineLet's calculate the x-coordinate of the vertex.\newlinex-coordinate = −b2a-\frac{b}{2a} = −42⋅1-\frac{4}{2\cdot 1} = −42-\frac{4}{2} = −2-2
  2. Find y-coordinate: Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x=−2x = -2 into the original equation.\newliney=(−2)2+4∗(−2)−2y = (-2)^2 + 4*(-2) - 2\newliney=4−8−2y = 4 - 8 - 2\newliney=−6y = -6
  3. Determine vertex point: We have found the xx-coordinate and yy-coordinate of the vertex. Therefore, the vertex of the parabola is at the point (−2,−6)(-2, -6).

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