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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)+5 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=x2+5 y=x^{2}+5 \newlineAnswer:

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Full solution

Q. Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=x2+5 y=x^{2}+5 \newlineAnswer:
  1. Use Vertex Formula: 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} for the xx-coordinate of the vertex. In this case, the equation is y=x2+5y = x^2 + 5, which means a=1a = 1 and b=0b = 0.
  2. Calculate x-coordinate: Since b=0b = 0, the formula simplifies to x=−0/(2⋅1)=0x = -0/(2\cdot1) = 0. This is the xx-coordinate of the vertex.
  3. Substitute xx into equation: To find the yy-coordinate of the vertex, we substitute the xx-coordinate back into the original equation. So we substitute x=0x = 0 into y=x2+5y = x^2 + 5.
  4. Calculate y-coordinate: Substituting x=0x = 0 gives us y=(0)2+5=0+5=5y = (0)^2 + 5 = 0 + 5 = 5. This is the y-coordinate of the vertex.
  5. Find Vertex Coordinates: Therefore, the coordinates of the vertex of the parabola y=x2+5y = x^2 + 5 are (0,5)(0, 5).

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