SOLUTION: I'm not sure I understand what they are asking us to do for this problem. Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist f

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Question 173145This question is from textbook intro algebra
: I'm not sure I understand what they are asking us to do for this problem. Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation.
y = x^2 + 8x + 16 This question is from textbook intro algebra

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure I understand what they are asking us to do for this problem. Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation.
y = x^2 + 8x + 16
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d = b^2 - 4ac
d = 64 - 4*1*16
d = 0
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The onsite solver explains it well.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%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=%288%29%5E2-4%2A1%2A16=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%288%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B8x%2B16+=+%28x--4%29%2A%28x--4%29

Again, the answer is: -4, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B16+%29