Question 95122: I am confused about this question. I have a graph with points (-1,0), (0.67,0) and (-0.16,-2) which is the vertex. I'm supposed to comment on the discriminant and form a quadratic equation and solve it. I came up with several equations which are not correct. Can someone help me? Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I am confused about this question. I have a graph with points (-1,0), (0.67,0) and (-0.165,-2) which is the vertex. I'm supposed to comment on the discriminant and form a quadratic equation and solve it. I came up with several equations which are not correct.
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Plot those points and you will see the vertex is below the x-axis and the
parabola has two Real Number zeroes: x=-1 and x=0.67
So the discriminant, b^2-4ac, must be greater than zero.
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With zeros at x=-1 and x = 0.67
f(x) = a(x+1)(x-0.67)
But the vertex says f(-0.165)=-2
So -2 = a(-0.165+1)(-0.165-0.67)
-2 = a*0.835*-0.835
a = 0.8685
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EQUATIOn:
f(x)= 2.8685..(x+1)(x-0.67)
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Cheers,
Stan H.
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