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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=4x^(2)+32 x+52 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=4x2+32x+52 y=4 x^{2}+32 x+52 \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=4x2+32x+52 y=4 x^{2}+32 x+52 \newlineAnswer:
  1. Calculate x-coordinate: To find the vertex of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c, we can use the vertex formula x=−b2ax = -\frac{b}{2a} to find the x-coordinate of the vertex.\newlineHere, a=4a = 4 and b=32b = 32.\newlineLet's calculate the x-coordinate of the vertex.\newlinex=−b2a=−322⋅4=−328=−4x = -\frac{b}{2a} = -\frac{32}{2\cdot4} = -\frac{32}{8} = -4
  2. Substitute x-coordinate: Now that we have the x-coordinate of the vertex, we can substitute it back into the original equation to find the y-coordinate of the vertex.\newlineLet's substitute x=−4x = -4 into y=4x2+32x+52y = 4x^2 + 32x + 52.\newliney=4(−4)2+32(−4)+52y = 4(-4)^2 + 32(-4) + 52\newliney=4(16)−128+52y = 4(16) - 128 + 52\newliney=64−128+52y = 64 - 128 + 52\newliney=−64+52y = -64 + 52\newliney=−12y = -12
  3. Find vertex coordinates: We have found the xx-coordinate and the yy-coordinate of the vertex. Therefore, the coordinates of the vertex are (−4,−12)(-4, -12).

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