SOLUTION: Find the x intercepts for the parabola y = x2 – 6x + 5. Find the vertex of the parabola y = - 2x2 + 8x + 4

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Question 212102: Find the x intercepts for the parabola y = x2 – 6x + 5.
Find the vertex of the parabola y = - 2x2 + 8x + 4


Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x intercepts for the parabola y = x2 – 6x + 5.
Step 1. For this problem y=0 since we want x-intercepts.

Step 2. Use quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where a=1, b=-6 and c= 5
Step 3. The following steps shows how to solve the above equation in Step 2 where you will find x=1 and x=5. Note the parabola intercepts x-axis when y=6 at these points.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B5+=+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=%28-6%29%5E2-4%2A1%2A5=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%28-6%29-sqrt%28+16+%29%29%2F2%5C1+=+1

Quadratic expression 1x%5E2%2B-6x%2B5 can be factored:
1x%5E2%2B-6x%2B5+=+1%28x-5%29%2A%28x-1%29
Again, the answer is: 5, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B5+%29





Problem: Find the vertex of the parabola y = - 2x2 + 8x + 4

+-2x%5E2%2B8x%2B4

Step 1. Graph is shown below and the vertex is at (2,12)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B8x%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=%288%29%5E2-4%2A-2%2A4=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+96+%29%29%2F2%5C-2+=+-0.449489742783178
x%5B2%5D+=+%28-%288%29-sqrt%28+96+%29%29%2F2%5C-2+=+4.44948974278318

Quadratic expression -2x%5E2%2B8x%2B4 can be factored:
-2x%5E2%2B8x%2B4+=+-2%28x--0.449489742783178%29%2A%28x-4.44948974278318%29
Again, the answer is: -0.449489742783178, 4.44948974278318. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B8%2Ax%2B4+%29



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