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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 1.33333333333333, 1.33333333333333. Here's your graph:


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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


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