document.write( "Question 40499: Could someone please help explain to me how to figue this problem?\r
\n" ); document.write( "\n" ); document.write( "h(x) = -3x^2
\n" ); document.write( " I need to state the domain and range of this quadratic function as well as its solution set in interval notation. Any ideas? \n" ); document.write( "

Algebra.Com's Answer #25892 by Nate(3500) $\"\"$ $\"About$

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: $\"y%3C=0\"$ .
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

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:
\n" ); document.write( "
\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%280%29%5E2-4%2A-3%2A0=0\"$ .
\n" ); document.write( "
\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: $\"x+=+%28-%280%29%29%2F2%5C-3\"$ .
\n" ); document.write( " Expression can be factored: $\"-3x%5E2%2B0x%2B0+=+-3%28x-0%29%2A%28x-0%29\"$
\n" ); document.write( "
\n" ); document.write( " Again, the answer is: 0, 0.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B0%2Ax%2B0+%29\"$

\n" ); document.write( " \n" ); document.write( "

\n" );