SOLUTION: Find the vertex and intercepts for each parabola. Sketch the graph. G(x) = x� + x � 6

Question 150542: Find the vertex and intercepts for each parabola. Sketch the graph.
G(x) = x� + x � 6

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Vertex:

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Multiply 2 and to get .

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Start with the given equation.

Plug in .

Square to get .

Combine the fractions.

So the y-coordinate of the vertex is .

So the vertex is

which in decimal form is (-0.5, -6.25).

Intercepts:

X-intercept(s):

Start with the given equation.

Plug in

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

This means that the x-intercepts are (-3,0) and (2,0)

-------------

Y-intercept:

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Combine like terms.

So the y-intercept is (0,-6)

============================================

Summary:

So the vertex is

which in decimal form is (-0.5, -6.25)

The x-intercepts are (-3,0) and (2,0) and the y-intercept is (0,-6)

Plot these points on the coordinate system

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Graph:

Now draw a parabola through all of the points to graph :

Graph of
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