SOLUTION: I need to know how to find the vertex and intercepts for a parabola and sketch it. The equation is g(x)=x2+x-6

Question 118068: I need to know how to find the vertex and intercepts for a parabola and sketch it. The equation is g(x)=x2+x-6
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
o find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)
To find the axis of symmetry, use this formula:

From the equation we can see that a=1 and b=1

Plug in b=1 and a=1

Multiply 2 and 1 to get 2

So the axis of symmetry is

So the x-coordinate of the vertex is (which is in decimal form). Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate

Start with the given polynomial

Plug in

Raise -0.5 to the second power to get 0.25

Combine like terms

So the vertex is (-0.5,-6.25)

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

To find the x-intercepts, set the whole function equal to zero and solve for x.

Start with the given equation

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our answer is
or

Notice if we graph we can see that the roots are and . We can also see that the vertex is (-0.5,-6.25). So this visually verifies our answer.

Graph of with the x-intercepts and and the vertex (-0.5,-6.25).

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The x-intercepts occur where
The y-intercepts occur where
First set

This is true if either
1st x-intercept
or
2nd x-intercept
These are called the roots of the equation. The co-
ordinate of the vertex is exactly midway between them, so
it,s at V(-(1/2), ). Now find g(-(1/2))
(Notice that if I add to , I get
and if I subtract from it, I get
as I should)

So the vertex is at (-1/2 , -25/4) answer
The y-intercept is at

So the y-intercept is at (0 , -6) answer
Here's the sketch

RELATED QUESTIONS
Find the vertex and intercepts for each parabola. Sketch the graph. G(x) = x� + x � 6 (answered by jim_thompson5910)
Find the vertex and intercepts for each parabola. Sketch the graph 44. g(x) = x^2 + x... (answered by funmath)
Find the vertex and intercepts for the parabola. Sketch the graph.... (answered by jim_thompson5910)
Find the vertex and intercepts for the parabola g(x)=x^2+x-6 Sketch the... (answered by solver91311)
find the vertex and intercepts for each parabola. sketch the graph... (answered by venugopalramana)
Find the vertex and intercepts for each parabola. Sketch the graph. g(x) = x^2 + x -... (answered by Paul)
Find the vertex and intercepts for each parabola. Sketch the graph.... (answered by stanbon)
Find the vertex and intercepts for each parabola. Sketch the graph. g(x) = x^2 + x -... (answered by checkley71)
I need your help. Can someone please graph this for me? Find the vertex and intercepts (answered by Alwayscheerful)