# What is the axis of symmetry and vertex for the graph y=x^2-8x+3?

Apr 20, 2016

color(blue)("Vertex"->(x,y)->(4,-13)
$\textcolor{b l u e}{\text{Axis of symmetry} \to x = 4}$

#### Explanation:

Standard form:$\text{ } y = a {x}^{2} + b x + c$

Write as:$\text{ } y = a \left({x}^{2} + \frac{b}{a} x\right) + c$

With a quadratic, the axis of symmetry passes through ${x}_{\text{vertex}}$

In the case of this question $a = 1$

color(blue)(x_("vertex")=(-1/2)xxb/a " "-> (-1/2)xx(-8)=+4)
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By substitution:

$\textcolor{b l u e}{{y}_{\text{vertex}} = {\left(4\right)}^{2} - 8 \left(4\right) + 3 = - 13}$
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color(blue)("Vertex"->(x,y)->(4,-13)
$\textcolor{b l u e}{\text{Axis of symmetry} \to x = 4}$