Question 164051: I have a graph that has an x-axis of (0.67, 0), an x-axis of (-1, 0) and a y-axis of (0, -2). I am instructed to look at the graph and comment on the sign of the discriminant. Form the quadratic equation based on teh information provided and find its solution. The graph lines point down and open up. Please help. Your help is extremely valuable and I really appreciate your time and attention. I know that the quadratic formula is ax^2+bx+c where a does not equal 0 is the equation formula but I don't know which numbers to use as a, b, and c.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I have a graph that has an x-axis of (0.67, 0), an x-axis of (-1, 0) and a y-axis of (0, -2). I am instructed to look at the graph and comment on the sign of the discriminant.
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You have two real roots so the discriminant is positive
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Form the quadratic equation based on the information provided and find its solution. The graph lines point down and open up. Please help. Your help is extremely valuable and I really appreciate your time and attention. I know that the quadratic formula is ax^2+bx+c where a does not equal 0 is the equation formula but I don't know which numbers to use as a, b, and c.
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One way to do this problem is as follows:
The y-intercept is given, so c = -2.
You have two roots so:
k(x-0.67)(x+1) = 0
k[x^2 + 0.33x -0.67] = 0
So -0.67k = -2
k = 2.9851
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Then y = 2.9851x^2 + 0.9851x - 2
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Another way to find the equation would be to substitute each of your
three point values into the quadratic form to get three equations in
a,b,and c. Then solve the systme of equations for the variables.
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Cheers,
Stan H.
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