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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. y=2x^(2)+12 x+36 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=2x2+12x+36 y=2 x^{2}+12 x+36 \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=2x2+12x+36 y=2 x^{2}+12 x+36 \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=2a = 2 and b=12b = 12.\newlineLet's calculate the x-coordinate of the vertex.\newlinex=−b2a=−122⋅2=−124=−3x = -\frac{b}{2a} = -\frac{12}{2\cdot2} = -\frac{12}{4} = -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.\newlineLet's substitute x=−3x = -3 into y=2x2+12x+36y = 2x^2 + 12x + 36.\newliney=2(−3)2+12(−3)+36y = 2(-3)^2 + 12(-3) + 36\newliney=2(9)−36+36y = 2(9) - 36 + 36\newliney=18−36+36y = 18 - 36 + 36\newliney=18y = 18
  3. Find vertex point: We have found the xx-coordinate and the yy-coordinate of the vertex. Therefore, the vertex of the parabola is at the point (−3,18)(-3, 18).

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