Ask a question


Graph the parabola


1 Answer by Expert Tutors

Tutors, sign in to answer this question.
Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)

     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.