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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)+4
Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an $(x, y)$ point. $\newline$ $y=x^{2}+4$ $\newline$ Answer:

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Find derivatives using logarithmic differentiation

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}+4

\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 $x = -\frac{b}{2a}$ . In this equation, $y = x^2 + 4$ , $a = 1$ and $b = 0$ , since there is no $x$ term.
Substitute Values: We substitute $a = 1$ and $b = 0$ into the vertex formula to find the $x$ -coordinate of the vertex. $\newline$ $x = -\frac{b}{2a} = -\frac{0}{2\cdot 1} = 0$
Calculate Y-coordinate: Now that we have the $x$ -coordinate of the vertex, we can substitute it back into the original equation to find the $y$ -coordinate. $y = x^2 + 4 = 0^2 + 4 = 4$
Find Vertex Coordinates: The coordinates of the vertex are $(x, y) = (0, 4)$ .

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