SOLUTION: Graph the parabola: y = (x-4)^2 - 2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Graph the parabola: y = (x-4)^2 - 2      Log On


   

Question 38733: Graph the parabola:
y = (x-4)^2 - 2
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+%28x-4%29%5E2+-+2
This parabola is in vertex form, so I can tell that it opens up and has a vertex of (4,-2). Next, pick some points and determine the y-value for each one. It should look like what is plotted below.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B14+=+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=%28-8%29%5E2-4%2A1%2A14=8.

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

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+5.41421356237309
x%5B2%5D+=+%28-%28-8%29-sqrt%28+8+%29%29%2F2%5C1+=+2.58578643762691

Quadratic expression 1x%5E2%2B-8x%2B14 can be factored:
1x%5E2%2B-8x%2B14+=+1%28x-5.41421356237309%29%2A%28x-2.58578643762691%29
Again, the answer is: 5.41421356237309, 2.58578643762691. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B14+%29