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y=(x-5)^(2)+1
Plot five points on the parabola: the vertex, two points to button.

$y=(x-5)^{2}+1$ $\newline$ Plot five points on the parabola: the vertex, two points to button.

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Transformations of quadratic functions

Full solution

Q.

y=(x-5)^{2}+1

\newline

Plot five points on the parabola: the vertex, two points to button.

Find Vertex: Find the vertex of the parabola. $\newline$ The vertex form of a parabola is $y=a(x-h)^2+k$ , where $(h,k)$ is the vertex. $\newline$ For $y=(x-5)^2+1$ , the vertex is $(5,1)$ .
Choose X-Values Right: Choose two $x$ -values to the right of the vertex to find corresponding $y$ -values. $\newline$ Let's pick $x=6$ and $x=7$ . $\newline$ Calculate $y$ when $x=6$ : $y=(6-5)^2+1 = 1^2+1 = 2$ . $\newline$ Calculate $y$ when $x=7$ : $y=(7-5)^2+1 = 2^2+1 = 5$ .
Choose X-Values Left: Choose two $x$ -values to the left of the vertex to find corresponding $y$ -values. $\newline$ Let's pick $x=4$ and $x=3$ . $\newline$ Calculate $y$ when $x=4$ : $y=(4-5)^2+1 = (-1)^2+1 = 2$ . $\newline$ Calculate $y$ when $x=3$ : $y=(3-5)^2+1 = (-2)^2+1 = 5$ .

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