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What is the vertex of $y = x^{2} - 2 x + 8$ $y= x^2-2x+8$ ?

1 Answer

Feb 16, 2016

vertex: $(x, y) = 1, 7)$ $(x,y)=1,7)$

Explanation:

The easiest way to find the vertex is to convert the given equation into "vertex form":
$XXX y = m {(x - a)}^{2} + b$ $color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)$
with a vertex at ( $a, b)$ $color(red)(a),color(blue)(b))$

Given
$XXX y = x^{2} - 2 x + 8$ $color(white)("XXX")y=x^2-2x+8$

Complete the square:
$XXX y = x^{2} - 2 x + 1 + 7$ $color(white)("XXX")y=x^2-2x+1 +7$

$XXX y = 1 {(x - 1)}^{2} + 7$ $color(white)("XXX")y=color(green)(1)(x-color(red)(1))^2+color(blue)(7)$
which is in "vertex-form".

graph{x^2-2x+8 [-3.684, 8.8, 5.06, 11.3]}

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