Graphing a Quadratic Function

1.    First of all you have to know that the equation of quadratic function is y=x² + qx + r.

2.    Mostly the quadratic function has intersection with x-axis and or y-axis. So you have to find it to make you easily draw the graph.

3.    You will get the x-axis intersection by substitute the function you have using y=0. Maybe you will get one point, two point or not both. If you didn’t get any point, it means that the graph is located under the x-axis or upper the x-axis without have intersection with the x-axis.

If you get one point, it means the point you get is the vertex of the graph. And if you get two points, it means the graph has two intersections with x-axis. Because the normally found is two points, let us use it to be example. We called the intersection point with (a,0) and (b,0)

4.    Find the y-axis intersection by substitute x=0 to the function. The meaning of y-axis intersection that you get is similar with the meaning of x-axis intersection. Because we already choose two intersection points at the x-axis intersection before, so the y-intersection is just one point. Let’s called it (0,c).

5.    The next step of graphing is finding the vertex. Vertex can be found by using formula. But don not worry if you forget the formula, you may use this step; use the x-axis or y-axis intersection to count the vertex, in case axis has two intersections point with the grapd. For instance, if you get two intersections at y-axis you have to use it. And if you get two intersections at x-axis, let’s use that point to find the vertex. In logic, when the graph passing through two point at x or y, the vertex coordinate of x-axis or y-axis will be located at the central of the two point. As I already say that we will use the two intersection of x-axis as example, so we have point a and b at x-axis. Count the differences of that two, and then divide it by two. We called the result x=d.

6.    Finding the x-coordinate of vertex, substitute the x=d for finding the y-vertex coordinate. Then call it y=e. Hence we have the vertex coordinate at (d,e)

7.    You already have points: (a,0), (b,0), (0,c), and (d,e). Try to figure out that point’s to the graph.

8.    If you still doubt about your graph, substitute independent x point or y point to the function so you will get another coordinate for accurate the graph.