I'm in algebra 2 at my high school, and I'm having more than a little trouble with the subject... currently, we are working with quadratic functions and graphing them. I know the three forms: standard- y=ax^2+bx+c Vertex- y= a(x-h)+k and intercept- y= (x-p)(x-q). However, I'm unsure of how to graph a parabola using just one of these equations. I know how to find the vertex/axis of symmetry... but not the other points. I just don't see how they come into play... please help!




also, we have been doing a lot of revenue word problems you know Y= (current customers - x)(cost + x)
and I don't know how to bring it from the equation to the maximum revenue without just substituting for x 20 times. Is there another way?

Well, from the first equation form, y = ax^2 + bx + c, there is not much you can do for graphing.

For the next one,

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

You know that (h, k) gives the vertex.
Putting x = 0, and solving for y, gives you the y-intercept.

Those two are enough to draw the graph :)

y = (x+p)(x+q)

The more general form, I believe is y = a(x+p)(x+q)

Now, you can only get the intercepts in this form, and the axis of symmetry, but not the actual coordinates of the maximum/minimum point without substituting more values.

In general, once you have 2 points, one being the vertex and the other a y-intercept, you can draw the curve without much calculation.

Otherwise, two coordinates are not enough, and you need a third point. This is because you don't know the y position of the vertex, due to the 'a' in front of the equation.


Let Current customers be a, and cost = b.

y = (a-x)(b+ x)

This is also:

y = -(x-a)(x+b)

Can you get the axis of symmetry there? :)