What is the axis of symmetry and vertex for the graph $F(x) = x ^ 2 - 4x - 5$ ?

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Answer 1 · 2017-09-06T10:56:47

This is not a conventional way to derive the answer. It uses part of the process for 'completing the square'.

Vertex $->(x,y)=(2,-9)$
Axis of symmetry $->x=2$

Consider the standard form of $y=ax^2+bx+c$

Write as : $y=a(x^2+b/a x) +c$

$x_("vertex")="axis of symmetry" = (-1/2)xxb/a$

The the context of this question $a=1$

$x_("vertex")="axis of symmetry" = (-1/2)xx(-4)/1 = +2$

So by substitution

$y_("vertex")=(2)^2-4(2)-5 = -9$

Thus we have:

Vertex $->(x,y)=(2,-9)$
Axis of symmetry $->x=2$

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What is the axis of symmetry and vertex for the graph F(x) = x ^ 2 - 4x - 5F(x) = x ^ 2 - 4x - 5?