1. 10
Quadratic Equations 10

2. 10.4 Graphing Quadratic Equations
Objectives
1. Graph quadratic equations. 2. Find the vertex of a parabola.

3. Graph Quadratic Equations
Example 1 Graph y = x2. x y –3 9 –2 4 –1 1 2 3
Make a table of values.
Plot these points and connect them with a smooth curve.

4. Graph Quadratic Equations
The curve in Example 1 is called a parabola.
The point (0,0), the lowest point on this graph, is called the vertex of the parabola.
The vertical line through the vertex (the y-axis here) is called the axis of the parabola. The axis of a parabola is a line of symmetry for the graph, because if the graph is folded on this line, the two halves will coincide.
Every equation of the form y = ax2 + bx + c, with
a ≠ 0, has a graph that is a parabola. Because of
its many useful properties, the parabola occurs frequently in real-life applications.

5. Find the Vertex of a Parabola
Generalization The x-coordinates of the x-intercepts for
y = ax2 + bx + c, by the quadratic formula, are

6. Find the Vertex of a Parabola
Generalization (cont.) Thus, the x-value of the vertex is

7. Find the Vertex of a Parabola
Example 4 Graph y = x2 + 6x + 5.
Step 1 Find the coordinates of the vertex.
The vertex is (–3,–4).

8. Finding the Vertex of a Parabola
Example 4 (continued) Graph y = x2 + 6x + 5.
Step 2 Find the y-intercept.
The y-intercept is (0,5).

9. Finding the Vertex of a Parabola
Example 4 (continued) Graph y = x2 + 6x + 5.
Step 3 Find the x-intercepts.
The x-intercepts are (–1,0) and (–5,0). 9

10. Find the Vertex of a Parabola
Example 4 (concluded) Graph y = x2 + 6x + 5.
Steps 4-5 Plot the points and sketch the graph.
The point (–6,5) is on the graph because it is the mirror image of the y-intercept across the parabola’s line of symmetry x = –3.