SOLUTION: Find the vertex and intercepts for this parabola: g(x) = x^2 + x - 6 This is how I have worked it: a = 1, b = 1, c = -6 x = -b/2a x = -1/[2(1)] = -1/2 g(-1/2) = (-1/2

Question 148000: Find the vertex and intercepts for this parabola:
g(x) = x^2 + x - 6
This is how I have worked it:
a = 1, b = 1, c = -6
x = -b/2a
x = -1/[2(1)] = -1/2
g(-1/2) = (-1/2)^2 + (-1/2) - 6
= 25/2
So, the vertex is (-1/2, 25/2)
Am I correct so far?
How do I verify that I am correct? What should my next step be?
I appreciate your help very much! Thank you!

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 .

Plug in .

Square to get .

Combine like terms.

So the vertex is

note: you can verify this with a calculator. You can use the "min/max" feature.

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

Intercepts:

x-intercept:

To find the x-intercept, plug in and solve for x

Start with the given equation.

Plug in

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

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

y-intercept:

To find the y-intercept, plug in and simplify

Start with the given equation.

Plug in

Simplify

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

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

Notice if we graph we can visually verify our answers.

Graph of

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