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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. y=4x^(2)+24 x+48 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=4x2+24x+48 y=4 x^{2}+24 x+48 \newlineAnswer:

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Q. Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=4x2+24x+48 y=4 x^{2}+24 x+48 \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=24b = 24.\newlineLet's calculate the x-coordinate of the vertex.\newlinex=−b2a=−242⋅4=−248=−3x = -\frac{b}{2a} = -\frac{24}{2\cdot4} = -\frac{24}{8} = -3
  2. Substitute xx into equation: Now that we have the xx-coordinate of the vertex, we can substitute it back into the original equation to find the yy-coordinate of the vertex.\newlineSubstitute x=−3x = -3 into y=4x2+24x+48y = 4x^2 + 24x + 48.\newliney=4(−3)2+24(−3)+48y = 4(-3)^2 + 24(-3) + 48\newliney=4(9)−72+48y = 4(9) - 72 + 48\newliney=36−72+48y = 36 - 72 + 48\newliney=12y = 12
  3. Find vertex coordinates: We have found the xx-coordinate and yy-coordinate of the vertex. Therefore, the coordinates of the vertex are (−3,12)(-3, 12).

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