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How do I grapgh the function that has the following properties: concave up, y-intercept is -6, zeros at x = -2 and x = 3?
\n" ); document.write( "This sounds a lot like a U shaped parabola which are formed by quadratic equations.
\n" ); document.write( "It's zeros are -2 and 3, so it can be said that:
\n" ); document.write( "x=-2
\n" ); document.write( "x+2=-2+2
\n" ); document.write( "x+2=0
\n" ); document.write( "and
\n" ); document.write( "x=3
\n" ); document.write( "x-3=3-3
\n" ); document.write( "x-3=0
\n" ); document.write( "A quadratic equation can be made of f(x)=(x+2)(x-3) that makes the parabola go through the x axis at -2 and 3. If we foil the parenthesis we get:
\n" ); document.write( "f(x)=x(x-3)+2(x-3)
\n" ); document.write( "f(x)=x^2-3x+2x-6
\n" ); document.write( "f(x)=x^2-x-6
\n" ); document.write( "Notice that if x=0, you'll have a y-intercept of -6.
\n" ); document.write( "Also, x^2 is positive so our parabola opens up.
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Notice this graph meets all of your requirements.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "