SOLUTION: Using the discriminant, determine the number of x-intercepts the graph of the equation will have. Do not graph the equation. y = x^2 + 12x + 36

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Using the discriminant, determine the number of x-intercepts the graph of the equation will have. Do not graph the equation. y = x^2 + 12x + 36      Log On


   

Question 247389: Using the discriminant, determine the number of x-intercepts the graph of the equation will have. Do not graph the equation.
y = x^2 + 12x + 36
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2%2B12x%2B36
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Can this be factored?
Yes.
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You also can use the quadratic formula:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B36+=+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=%2812%29%5E2-4%2A1%2A36=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2812%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B12x%2B36+=+1%28x--6%29%2A%28x--6%29

Again, the answer is: -6, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B36+%29