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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+4
Answer:

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

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Find the axis of symmetry of a parabola

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}-2 x+4

\newline

Answer:

Identify general form: Identify the general form of the quadratic equation. $\newline$ The given parabola is in the form $y = ax^2 + bx + c$ , where $a = 1$ , $b = -2$ , and $c = 4$ .
Use vertex formula: Use the vertex formula for a parabola. $\newline$ The vertex of a parabola $y = ax^2 + bx + c$ is given by the point $(h, k)$ , where $h = -\frac{b}{2a}$ and $k$ is the $y$ -value when $x = h$ .
Calculate x-coordinate: Calculate the x-coordinate of the vertex $h$ . For the given equation $y = x^2 - 2x + 4$ , $a = 1$ and $b = -2$ . $h = -(-2)/(2\cdot1) = 2/2 = 1$
Calculate y-coordinate: Calculate the y-coordinate of the vertex $k$ . Substitute $x = h$ into the original equation to find $k$ . $k = (1)^2 - 2*(1) + 4 = 1 - 2 + 4 = 3$
Combine coordinates: Combine the coordinates to form the vertex point. $\newline$ The vertex of the parabola is at the point $(h, k) = (1, 3)$ .

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