Question

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

Answer 1

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.

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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`