How do you graph and label the vertex and axis of symmetry of y=(x-2)^2-1?

1 Answer
Mar 3, 2017

Vertex ->(x,y)=(2,-1)

Axis of symmetry is x=2

x_("intercept")->x=1 and x=3

y_("intercept")=3

Explanation:

This the vertex format of a quadratic equation.

If you were to multiply it all out the x^2 term would be positive.

Thus the graph is of general shape uu.

On the other hand, it had been negative then the shape would have been nn
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The axis of symmetry is the x value of the vertex

We can virtually read the vertex off directly but with a small adjustment.

#x_("vertex")=(-1)xx(-2) = +2

y_("vertex")=-1

Vertex ->(x,y)=(2,-1)

So axis of symmetry is x=2

THERE IS NO DIRECT REQUEST TO DETERMINE THE AXIS INTERCEPTS.

To ul("sketch") this graph you would need to determine these.

Tony BTony B
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y=(x-2)^2-1

At the x-intercepts y=0 giving:

(x-2)^2=1

x-2=+-sqrt(1)=+-1

x=+-1+2

x=1 and x=3

At the y intercept x=0

y=(0-2)^2-1

y=+3