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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.
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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)
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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)
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Notice if we graph we can visually verify our answers.
Graph of 
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