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)
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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).
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
(