SOLUTION: I am very confused on how to find the vertex and points of a Parabola then when i graph it, the parabola always has a straight line on one side. How am I supposed to solve and grap

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I am very confused on how to find the vertex and points of a Parabola then when i graph it, the parabola always has a straight line on one side. How am I supposed to solve and grap      Log On


   

Question 306854: I am very confused on how to find the vertex and points of a Parabola then when i graph it, the parabola always has a straight line on one side. How am I supposed to solve and graph 2x^2-13x-7=0?
Found 2 solutions by texttutoring, Fombitz:
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
You have to Complete the Square to change its form.

Look in your book at how to complete the square (if you don't already know).
It should end up looking like this:

2(x-13/4)^2 - 225/8 = 0

So the vertex is at (13/4, -225/8)

Let me know if you need any clarifications.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First complete the square to get to vertex form,
2x%5E2-13x-7=0
2%28x%5E2-%2813%2F2%29x%29-7=0
To complete the square, take (1/2) of the x-coefficient, square it, and then add it to both sides.
Since this is going on inside the parenthese, make sure to multiply by 2 to add the right hand value.
%281%2F2%29%2813%2F2%29=13%2F4
%2813%2F4%29%5E2=169%2F16
2%28x%5E2-%2813%2F2%29x%2B169%2F16%29-7=2%28169%2F16%29
2%28x-%2813%2F4%29%29%5E2-7=169%2F8%29
2%28x-%2813%2F4%29%29%5E2-56%2F8-169%2F8=0%29
2%28x-%2813%2F4%29%29%5E2-56%2F8-169%2F8=0%29
2%28x-%2813%2F4%29%29%5E2-225%2F8=0%29
Now the equation is in vertex form.
The vertex is (13%2F4,-225%2F8)
The y-intercept, from the original equation is, -7.

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Straight line on one side, what does that mean?
The axis of symmetry makes a mirror of the graph.
So then
f%2813%2F4%2B1%29=f%2813%2F4-1%29
f%2813%2F4%2B2%29=f%2813%2F4-2%29
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So then you only have to solve for one of those y coordinates and you'll have both.