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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 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=2x2−12 y=2 x^{2}-12 \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=2x2−12 y=2 x^{2}-12 \newlineAnswer:
  1. Identify Coefficients: 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}. In this equation, y=2x2−12y = 2x^2 - 12, there is no bxbx term, so b=0b = 0.
  2. Calculate x-coordinate: Using the vertex formula x=−b2ax = -\frac{b}{2a}, we substitute b=0b = 0 and a=2a = 2 into the formula to find the x-coordinate of the vertex.\newlinex=−02⋅2x = -\frac{0}{2\cdot 2}\newlinex=0x = 0
  3. Find y-coordinate: Now that we have the x-coordinate of the vertex, we need to find the corresponding y-coordinate by substituting xx back into the original equation.y=2(0)2−12y = 2(0)^2 - 12y=−12y = -12
  4. Vertex Coordinates: The coordinates of the vertex are therefore (0,−12)(0, -12).

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