Graph the parabola

y = (x + 4)^{2} - 4

Notice that this is the vertex form of the equation of a parabola which is generally expressed as follows:

y = a(x - h)^{2} + k ,

where (h, k) is the vertex of the parabola and 'a' determines whether the parabola opens upward (if a>0, or positive) or downwards (if a<0, or negative).

For the equation of the parabola in question,

y = (x + 4)^{2} - 4 ==> y = (x - (-4))^{2} + (-4)

we find that its vertex is at (h, k) = (-4, -4) and its graph opens upwards since a = 1 > 0 (that is, since a is positive).

To graph the parabola, we plot the vertex (-4, -4). Since it opens up, we know that the range of the parabola consists of all values of y such that y>-4 (i.e., the minimum value of y is -4). So you can either find points by plugging in a few values for y that are greater than -4 to find their x values, or you can find values of y by plugging in a few values of x. Also note that, when given the equation in vertex form, the axis of symmetry of the parabola is the line x = h, which in this case would be x = -4.

Unless you need to plot specific points, you can typically just plot the vertex and draw a general form of the graph given that it opens up or down.

## Comments

cant answer... the equation can be read 2 different ways.

1) [(x+4)^2] -4

or

2)(x+4)^(2-4)

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html