Question 669418
Graph the following quadratic equation {{{ F(x)=x^2+4x }}}
The graph of quadratic equations are parabolas.
The best way to do this is convert the equation to a form which will give you information with which you can draw the graph. The standard form of equation for a parabola, y=a(x-h)^2+k, which you just learned is such a form. It provides you with the following information:
(h,k)=(x,y) coordinates of the vertex.
axis of symmetry
if a>0, the parabola opens upwards, curve has a minimum
if a<0, the parabola opens downwards, curve has a maximum
..
For given equation:
F(x)=x^2+4x
complete the square
F(x)=(x^2+4x+4)-4
F(x)=(x+2)^2-4
This is an equation of a parabola that opens upwards(a=1)
Its vertex: (-2,-4) minimum of -4 at x=-2
axis of symmetry: x=-2
x-intercept:
set y=0
x^2+4x=0
x(x+4)=0
x=0
and
x=-4
you now have the information needed to draw the graph of the parabola.
see the following graph below:
{{{ graph( 300, 300, -10, 10, -10, 10, x^2+4x) }}}