What is the axis of symmetry and vertex for the graph $y = x^2 - 4x + 1$ ?

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Answer 1 · 2017-04-15T18:52:23

$x = 2$ is the line of symmetry.

$(2,-3)$ is the vertex.

Find the axis of symmetry first using $x = (-b)/(2a)$

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

$x= (-(-4))/(2(a)) = 4/2 = 2$

The vertex lies on the line of symmetry, so we know $x = 2$
Use the value of $x$ to find $y$

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

$y = 4-8+1 = -3$

The vertex is at $(2,-3)$

You can also use the method of completing the square to write the equation in vertex form: $y= a(x+b)^2 +c$

$y = x^2 -4x color(blue)(+4-4) +1" "[color(blue)(+(b/2)^2-(b/2)^2)]$

$y = (x-2)^2 -3$

The vertex is at $(-b,c) = (2,-3)$

What is the axis of symmetry and vertex for the graph y = x^2 - 4x + 1y = x^2 - 4x + 1?