SOLUTION: Could someone please help explain to me how to figue this problem? h(x) = -3x^2 I need to state the domain and range of this quadratic function as well as its solution set

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Could someone please help explain to me how to figue this problem? h(x) = -3x^2 I need to state the domain and range of this quadratic function as well as its solution set       Log On


   

Question 40499: Could someone please help explain to me how to figue this problem?
h(x) = -3x^2
I need to state the domain and range of this quadratic function as well as its solution set in interval notation. Any ideas?
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex is at the origin. Since a is negative, the parabola opens down. The domain: all real values .... The range: y%3C=0.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B0x%2B0+=+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%2A0=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%280%29%29%2F2%5C-3.
Expression can be factored: -3x%5E2%2B0x%2B0+=+-3%28x-0%29%2A%28x-0%29

Again, the answer is: 0, 0. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B0%2Ax%2B0+%29