SOLUTION: For quadratic functions, sketch two parabolas showing all procedures (concavity, y-intercepts, x-intercepts, symmetric axis and vertex point) A) {{{y= 3x^2 -4x +1}}} B) {{{y=

Algebra ->  Graphs -> SOLUTION: For quadratic functions, sketch two parabolas showing all procedures (concavity, y-intercepts, x-intercepts, symmetric axis and vertex point) A) {{{y= 3x^2 -4x +1}}} B) {{{y=      Log On


   

Question 39546: For quadratic functions, sketch two parabolas showing all procedures (concavity, y-intercepts, x-intercepts, symmetric axis and vertex point)
A) y=+3x%5E2+-4x+%2B1
B) y=+-2x%5E2+%2Bx+%2B1
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A)(y= 3x^2 -4x +1}}}
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-4x%2B1+=+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=%28-4%29%5E2-4%2A3%2A1=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+4+%29%29%2F2%5C3+=+1
x%5B2%5D+=+%28-%28-4%29-sqrt%28+4+%29%29%2F2%5C3+=+0.333333333333333

Quadratic expression 3x%5E2%2B-4x%2B1 can be factored:
3x%5E2%2B-4x%2B1+=+3%28x-1%29%2A%28x-0.333333333333333%29
Again, the answer is: 1, 0.333333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B1+%29


B) y=+-2x%5E2+%2Bx+%2B1
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B1x%2B1+=+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=%281%29%5E2-4%2A-2%2A1=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+9+%29%29%2F2%5C-2+=+-0.5
x%5B2%5D+=+%28-%281%29-sqrt%28+9+%29%29%2F2%5C-2+=+1

Quadratic expression -2x%5E2%2B1x%2B1 can be factored:
-2x%5E2%2B1x%2B1+=+-2%28x--0.5%29%2A%28x-1%29
Again, the answer is: -0.5, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B1%2Ax%2B1+%29

Hope this helps.
Cheers,
Stan H.