At this point in our study we should be able to find x- and y-intercepts and solve any quadratic equation. Now we will learn an easy method used to graph them. The graph of a quadratic equation is called a parabola.
The more points we plot the easier it is to see that the graph is u-shaped. The vertex, in this case, is the point where the graph changes from decreasing to increasing, or the point with the smallest y-value. Here the vertex is (0, 0) which is also the x- and y-intercept. The line x = 0, the y-axis, is the line of symmetry. This is the line where we could fold our paper to see that the two sides of the graph coincide.
Line of symmetry: x = 1
x-intercepts: (-2,0) and (4,0)
y-intercept: (0, -8)
Vertex: (1, -9)
5th point: (2, -8)
Recall that two points determine a line - this is not the case for parabolas. Parabolas require a minimum of 3 points but we usually want to find at least five points to make a nice graph. Find the vertex, x- and y- intercepts as well as the line of symmetry.
Tip: The axis of symmetry of any quadratic function will be the vertical line
Graph and label all important points: