How do you write $F(x)=x^2-2x+5$ in vertex form?

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Answer 1 · 2017-06-20T06:13:49

$y=(x-1)^2+4$

Given -

$F(x)=x^2-2x+5$

$y=x^2-2x+5$

Vertex

x - coordinate of the vertex

$x=(-b)/(2a)=(-(-2))/(2 xx 1)=2/2=1$

y - coordinate

$y=(1)^2-2(1)+5=1-2+5=4$

Vertex $(1,4)$

Parabola in vertex form

$y=a(x-h)^2+k$

Where -

$a=1$ ----- coefficient of $x^2$
$h=1$ --- x - coordinate of the vertex
$k=4$ --- y - coordinate of the vertex

Substitute these values into the equation.

$y=1(x-1)^2+4$
$y=(x-1)^2+4$
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How do you write F(x)=x^2-2x+5F(x)=x^2-2x+5 in vertex form?