# Math Help - Functions?

1. ## Functions?

Hey, just working on some functions and ive got a couple ive never seen before. I need to know how to get the numbers to draw the function and the domain and range.

y = (x - 2)^2 - 5

y = 3x^2 - x - 2

Any help is appreciated.

2. Originally Posted by Dannblood
Hey, just working on some functions and ive got a couple ive never seen before. I need to know how to get the numbers to draw the function and the domain and range.

y = (x - 2)^2 - 5

y = 3x^2 - x - 2

Any help is appreciated.
Parabolas are nice to graph. you need AT MOST 4 points to graph things like these.

To graph a parabola we need to find the x-intercepts, the y-intercepts, and the vertex.

To find the x-intercepts, we replace y with zero and solve for x.

To find the y-intercepts, we replace x with zero and solve for y

To find the vertex:

If the parabola is given in the form: $f(x) = y = ax^2 + bx + c$

the x-value for the vertex is given by: $x = \frac {-b}{2a}$

Thus the co-ordinate for the vertex is: $\left( \frac {-b}{2a}, f \left( \frac {-b}{2a} \right) \right)$

If the parabola is given in the form: $f(x) = y = a(x - h)^2 + k$

Then the vertex is given by: $(h,k)$

once you have these points, plot them on your graph and draw a curve thought them that looks like a parabola. Try the problems, if you need more help someone will help you

3. Jhevon's given you lots of great info. Like he said, parabolas are easy to graph once you have the hang of them. When you're new to them, they're especially simple when you have them in standard form: y = a(x-h)^2 + k, like your first example. When graphing this type of parabola, it's best to simply know your basic points for y = x^2. Those are of course: (0,0), (1,1), (2,4), (3,9), (4,16), (-1,1), (-2,4), (-3,9), (-4,16) and so on. Then you can plot these points (I usually do the first three) and draw the basic parabola, which is y = x^2.

From there, you know that h represents a horizontal shift: -h shifts it h units to the right, and +h shifts it h units to the left. The k represents vertical shifts: +k shifts it k units up, and -k shifts it k units downwards. So, simply move each point appropriately, then connect those new points as a parabola.