document.write( "Question 468755: Hi! I need help with two problems please? The only thing I am understanding is the minimum and maximum values. I cannot get the figures right.
\n" ); document.write( "Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function and graph the function.
\n" ); document.write( "f(x)=-2x^2+2x+4
\n" ); document.write( "f(x)= 1-x^2 \n" ); document.write( "

Algebra.Com's Answer #321633 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function and graph the function.
\n" ); document.write( "f(x)=-2x^2+2x+4
\n" ); document.write( "f(x)= 1-x^2
\n" ); document.write( "...
\n" ); document.write( "Standard form of parabola: y=婢(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
\n" ); document.write( "If the lead coefficient is>0, the parabola opens upwards and there is a minimum. If the lead coefficient is <0, the parabola opens downwards and there is a maximum. A is a multiplier which affects the steepness of the parabola.
\n" ); document.write( "..
\n" ); document.write( "f(x)=-2x^2+2x+4
\n" ); document.write( "completing the square
\n" ); document.write( "f(x)=-2(x^2-x+1/4)+4+1/2
\n" ); document.write( "f(x)=-2(x-1/2)^2+9/2
\n" ); document.write( "This is a parabola which opens downwards with vertex at (1/2,9/2). (maximum=9/2)
\n" ); document.write( "Axis of symmetry: x=1/2
\n" ); document.write( "..
\n" ); document.write( "f(x)= 1-x^2
\n" ); document.write( "f(x)=-x^2+1
\n" ); document.write( "Already in standard form,This is a parabola which opens downwards with vertex at (0,1). (maximum=1)
\n" ); document.write( "Axis of symmetry: x=0 or y-axis
\n" ); document.write( "See graph below as a visual check on answers
\n" ); document.write( "..\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C-2x%5E2%2B2x%2B4%2C-x%5E2%2B1%29+\"$ \n" ); document.write( "

\n" );