How do I graph a parabola?

You'd have to get x-values like -2, -1, 0, 1, and 2 and plug them into the equation. Then you just solve for y and plot the points. Like if you have x^2+2x+3 just substitute the x's for each value like (-1)^2+2(-1)+3.

Okay, so say your parabola is y=5x^2+3x+4. (2x^2 is Two x squared.)

The 1, 3, 5, 7 method is called "Step Pattern", and it is applied to the a value in your parabola, which in this case is 5. (y=ax^2+bx+c) <---a value in our example at the top is 5.

In a parabola with an a value of one, you would start at the origin (0,0) and go over one unit (both left and right, because a parabola has a branch on both sides) and then UP one unit. So then you put your points at (1,1) and (-1,1). Then you will go from those two points and move over another one unit then UP 3 units, so your next two points will be at (2,4) and (-2,4). Then you do it once more (move over ONE unit, then UP 5 units.) That's the step-pattern, because you moved up 1 unit the first time, then 3 units, then 5 units. (You don't usually include the 7, but you can if you like, I guess.)

So, back to the example I put, y=5x^2+3x+4 You simple multiply the a value by 1, 3, and five to get your NEW step-pattern. The a value in my example is 5, so you multiply 5 by 1, 3, and 5.

5x1=5, so you would move UP 5 units for the first step.

5x3=15, so you would move UP 15 units for the second step.

5x5=25, so you would move UP 25 units for the third step.

(Each left and right shift you make will always be ONE UNIT. The step-pattern focuses on the VERTICAL shifts, aka moving UP or DOWN.)

I REALLY hope this helped, and didn't confuse you too much.