SOLUTION: Use the discriminant to find how many places the quadratic function crosses the x-axis. y = 9x2 - 24x + 16

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Question 193812: Use the discriminant to find how many places the quadratic function crosses the x-axis.
y = 9x2 - 24x + 16
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use the discriminant to find how many places the quadratic function crosses the x-axis.
y = 9x2 - 24x + 16
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D = sqrt(576 - 576) = 0
So it "crosses" (actually is tangent to) the x-axis at 1 point.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-24x%2B16+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-24%29%5E2-4%2A9%2A16=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-24%29%29%2F2%5C9.
Expression can be factored: 9x%5E2%2B-24x%2B16+=+%28x-1.33333333333333%29%2A%28x-1.33333333333333%29

Again, the answer is: 1.33333333333333, 1.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-24%2Ax%2B16+%29


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Ignore the solver's factoring comments, and it doesn't get it exactly right if the coeff of the x^2 is not 1.
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x = 4/3