SOLUTION: Calculate the value of the discriminant of x2+4x+4=0 By examining the sign of the discriminant in part a, how many x-intercepts would the graph of x2+4x+4=0 have? Why? Thank

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Question 204457: Calculate the value of the discriminant of x2+4x+4=0
By examining the sign of the discriminant in part a, how many x-intercepts would the graph of x2+4x+4=0 have? Why?

Thanks so much!!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Calculate the value of the discriminant of x2+4x+4=0
By examining the sign of the discriminant in part a, how many x-intercepts would the graph of x2+4x+4=0 have? Why?
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The discriminant is b^2 - 4ac, which in this case is zero (0). That means there is one x-intercept - the x-axis is tangent to the curve at its vertex.
This is covered well by the onsite solver, too.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B4+=+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=%284%29%5E2-4%2A1%2A4=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%284%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B4x%2B4+=+%28x--2%29%2A%28x--2%29

Again, the answer is: -2, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B4+%29