# How do you sketch the graph of #y=x^2+8# and describe the transformation?

##### 2 Answers

See below

#### Explanation:

The first thing you need to find is the axis of symmetry by using

-b/2a

after you find that, use it to find the vertex of

In this case x should equal

so

giving just 8

the y-intercept is 8 as

the graph should look like this

graph{x^2+8 [-11.5, 8.5, 0.84, 10.84]}

it is a parabola.

Detailed explanation given

The transformation is that of

Vertex

Axis of symmetry

y-intercept = 8

x-intercept -> none

#### Explanation:

The first thing you need to determine is the general shape.

This is a quadratic equation so it has a horse shoe type shape.

The

,..................................................................................................

Consider the standardised equation form of

Write this as:

or the same thing in a different form:

Note that in the case of this question

So

Now compare

so

Thus the vertex coincides with the y-axis as does the axis of symmetry .

'.........................................................................

As the axis of symmetry is the y-axis set

As the vertex is at

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You do not need to work out a whole pile of points. Just make sure the general shape is

You do not need to draw to scale so it should only take about 5 to 15 seconds to complete ( some may take longer ). Do not forget to label your points and put a title on it.