Question 316882: I neeed help graphing f(x)=x^2-7x-8 I need to understand how to find the vertex, x-intercept,line of symmetry, and the opening of the graph.
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! y = x^2-7x-8
To find the x intercepts, simply set y=0 and solve for x (by factoring):
0=x^2-7x-8
0=(x-8)(x+1)
The x-intercepts are x=8 and x= -1.
The easiest way to graph it is to complete the square, to turn it into a form that is more easily graphed:
Completing the square:
y = x^2-7x-8 (halve the b term, -7, and then square it: (-7/2)^2 = 49/4)
y = x^2 -7x +49/4 - 8 - 49/4 (add 49/4 beside the b term, -7, but then subtract it after the -8 term)
y = (x - 7/2)^2 - 8 - 49/4
y = (x - 7/2)^2 - 81/4
So the vertex is at (7/2, -81/4)
It opens up (because the x^2 term is positive), and the line of symmetry is just the x-coordinate of the vertex, 7/2.
Hope that helps. Let me know if you're still stuck!
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