SOLUTION: Sketch the graph of the function y = 3 - 3x2. Label all intercepts.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Sketch the graph of the function y = 3 - 3x2. Label all intercepts.       Log On


   

Question 38642: Sketch the graph of the function y = 3 - 3x2. Label all intercepts.

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y = 3 - 3x^2
The vertex is: (-b/2a,f(x)) so the vertex is: (0,3)
Now, pick other points to plot .... should look like the graph below:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B0x%2B3+=+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=%280%29%5E2-4%2A-3%2A3=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+36+%29%29%2F2%5C-3+=+-1
x%5B2%5D+=+%28-%280%29-sqrt%28+36+%29%29%2F2%5C-3+=+1

Quadratic expression -3x%5E2%2B0x%2B3 can be factored:
-3x%5E2%2B0x%2B3+=+-3%28x--1%29%2A%28x-1%29
Again, the answer is: -1, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B0%2Ax%2B3+%29