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Graphing Quadratic Equations

Shown below is an of a quadratic equation, and its graph. In this lesson you will learn about quadratic functions, and how to graph them.

GRAPHING QUADRATIC EQUATIONS:

1. The first step of graphing a quadratic equation is to have a rough idea of how the graph should look like. A quadratic function is a parabola when graphed. The general formula for a quadratic equation is as follows:

The ax^2 is the quadratic term. The quadratic term must be present in order for the equation to be identified as a quadratic equation. In other words a quadratic equation must have x^2 in it.

The bx is the linear tem of the quadratic equation, and the c is the constant term in the quadratic equation.

EDUCATIONAL LINKS

Shown on the left is the graph of :

f(x) = 2x^2-1.

The first part of the equation is 2x, because the coefficient of x is positive the parabola is concave up. If the coefficient of x were to be negative then the parabola would be concave down.

The second part of the equation tells us the vertical shift of the equation. Since the vertical shift is negative 2, it means the graph is shifted 2 units down.

THINGS TO NOTICE

2. The next step is to find the vertex using the formula to find the vertex of the parabola.

The x, and y intercepts need to be computed to figure out where the line will touch the x, and/or y axis.

3. After finding the intercepts, it is recommended to create a table for the equation to plot a couple of additional points.

Below is step by step instructions of how to graph f(x)= -(x^2)+4:

1. Find the points of intersection.

2. The next, and final step is to plot the points of intersection, and connect a line through it. To make you graph more accurate you make also decide to create a table as shown below:

GENERIC QUADRATIC EQUATION