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

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

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Answer 1 · 2016-04-20T14:40:36

$Vertex \to (x, y) \to (4, - 13)$ $color(blue)("Vertex"->(x,y)->(4,-13)$
$Axis of symmetry \to x = 4$ $color(blue)("Axis of symmetry"->x=4)$

Explanation:

Standard form: $y = a x^{2} + b x + c$ $" "y=ax^2+bx+c$

Write as: $y = a (x^{2} + \frac{b}{a} x) + c$ $" "y=a(x^2+b/a x)+c$

With a quadratic, the axis of symmetry passes through $x_{vertex}$ $x_("vertex")$

In the case of this question $a = 1$ $a=1$

$x_{vertex} = (- \frac{1}{2}) \times \frac{b}{a} \to (- \frac{1}{2}) \times (- 8) = + 4$ $color(blue)(x_("vertex")=(-1/2)xxb/a " "-> (-1/2)xx(-8)=+4)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
By substitution:

$y_{vertex} = {(4)}^{2} - 8 (4) + 3 = - 13$ $color(blue)(y_("vertex")=(4)^2-8(4)+3 =-13)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Vertex \to (x, y) \to (4, - 13)$ $color(blue)("Vertex"->(x,y)->(4,-13)$
$Axis of symmetry \to x = 4$ $color(blue)("Axis of symmetry"->x=4)$

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

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Explanation:

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What is the axis of symmetry and vertex for the graph y=x2−8x+3y=x^2-8x+3?

1 Answer

Explanation:

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