How To Graph Points On The Coordinate Plane 10 Steps

The x-axis goes left and right, the second coordinate is on the y-axis. The y-axis goes up and down. Positive numbers go up or right (depending on the axis). Negative numbers go left or down.

Quadrant I gets (+,+); quadrant I is above and to the left of the y-axis. Quadrant IV gets (+,-); quadrant IV is below the x-axis and to the right of the y-axis. (5,4) is in quadrant I. (-5,4) is in Quadrant II. (-5,-4) is in Quadrant III. (5,-4) is in Quadrant IV.

Graph points from a line. Let’s say the equation is y = x + 4. So, pick a random number for x, like 3, and see what you get for y. y = 3 + 4 = 7, so you have found the point (3, 7). Graph points from a quadratic equation. Let’s say the equation of the parabola is y = x2 + 2. Do the same thing: pick a random number for x and see what you get for y. Picking 0 for x is easiest. y = 02 + 2, so y = 2. You have found the point (0, 2).

Unless you are only graphing a point, you will need at least two points. A line requires two points. A circle requires two points if one is the center; three if the center is not included (Unless your instructor has included the center of the circle in the problem, use three). A parabola requires three points, one being the absolute minimum or maximum; the other two points should be opposites. A hyperbola requires six points; three on each axis.

Modifying the x coordinate moves the equation left or right. Adding a constant moves the equation up or down. Turning it negative (multiplying by -1) flips it over; if it is a line, it will change it from going up to down or going down to up. Multiplying it by another number will either increase or decrease the slope.

y = (x-2)^2 is the same parabola, except it is graphed two spaces to the right of the origin; its base is now at (2,0). y = x^2 + 2 is still the same parabola, except now it is graphed two spaces higher at (0,2). y = -x^2 (the negative is applied after the exponent ^2) is an upside down y = x^2; its base is (0,0). y = 5x^2 is still a parabola, but it gets larger even faster, giving it a thinner look.