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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. y=x^(2)-2x-7 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=x2−2x−7 y=x^{2}-2 x-7 \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=x2−2x−7 y=x^{2}-2 x-7 \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 formula for the x-coordinate of the vertex, which is −b2a-\frac{b}{2a}.\newlineIn our equation, a=1a = 1 and b=−2b = -2.\newlineLet's calculate the x-coordinate of the vertex.\newlinex=−(−2)/(2⋅1)=22=1x = -(-2)/(2\cdot1) = \frac{2}{2} = 1
  2. Find y-coordinate: Now that we have the x-coordinate of the vertex, we need to find the corresponding y-coordinate by plugging x=1x = 1 into the original equation.y=(1)2−2∗(1)−7=1−2−7=−8y = (1)^2 - 2*(1) - 7 = 1 - 2 - 7 = -8
  3. Identify vertex point: We have found both coordinates of the vertex. The vertex of the parabola is at the point (1,−8)(1, -8).

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