SOLUTION: how do you graph y=(x-1)(x-4) show me the steps

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Question 38805: how do you graph y=(x-1)(x-4) show me the steps
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28x-1%29%28x-4%29
y=x%5E2-5x%2B4
Vertex: (2.5,-2.25)
The equation has a positive a value, so the parabola opens upwards. Pick points and graph them.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%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=%28-5%29%5E2-4%2A1%2A4=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+9+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%28-5%29-sqrt%28+9+%29%29%2F2%5C1+=+1

Quadratic expression 1x%5E2%2B-5x%2B4 can be factored:
1x%5E2%2B-5x%2B4+=+1%28x-4%29%2A%28x-1%29
Again, the answer is: 4, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B4+%29