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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 $(x, y)$ point. $\newline$ $y=x^{2}+5$ $\newline$ Answer:

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Complex conjugate theorem

Full solution

Q. Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an

(x, y)

point.

\newline

y=x^{2}+5

\newline

Answer:

Use Vertex Formula: To find the vertex of a parabola in the form $y = ax^2 + bx + c$ , we can use the vertex formula $x = -\frac{b}{2a}$ for the $x$ -coordinate of the vertex. In this case, the equation is $y = x^2 + 5$ , which means $a = 1$ and $b = 0$ .
Calculate x-coordinate: Since $b = 0$ , the formula simplifies to $x = -0/(2\cdot1) = 0$ . This is the $x$ -coordinate of the vertex.
Substitute $x$ into equation: To find the $y$ -coordinate of the vertex, we substitute the $x$ -coordinate back into the original equation. So we substitute $x = 0$ into $y = x^2 + 5$ .
Calculate y-coordinate: Substituting $x = 0$ gives us $y = (0)^2 + 5 = 0 + 5 = 5$ . This is the y-coordinate of the vertex.
Find Vertex Coordinates: Therefore, the coordinates of the vertex of the parabola $y = x^2 + 5$ are $(0, 5)$ .

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