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M098 Carson Elementary and Intermediate Algebra 3e Section 6.7 Objectives 1. 2. 2 Graph quadratic equations in the form y = ax + by + c (using a table). Graph quadratic functions (using a table). Vocabulary Axis of symmetry Vertex Parabola A line that divides a graph into two symmetrical halves. The lowest point on a parabola that opens up or highest point on a parabola that opens down. The shape of the graph of a quadratic equation. Prior Knowledge Graphing equations using a table of values. Function notation: y = f(x) Vertical line test New Concepts 2 1. Graph quadratic equations in the form y = ax + bx + c The graphing that we did earlier involved linear equations in two variables. The highest degree of any term was 1. The graph of a linear equation is a straight line. Now we want to look at the graphs of quadratic (degree 2) equations. One method that always works to graph an equation is to create a table of values. Example 1: Graph y = x x -2 -1 0 1 2 2 y 4 1 0 1 4 Axis: x = 0 Vertex (0, 0) The graph of every quadratic equation will be in the shape of a parabola. The axis of symmetry is the vertical line that divides the graph into two symmetrical halves. The vertex is the lowest or highest point of the parabola. Example 2: Graph x -2 1 0 1 2 V. Zabrocki y 9 3 1 3 9 2 y = 2x + 1 Axis: x = 0 Vertex: (0, 1) page 1 M098 Carson Elementary and Intermediate Algebra 3e Example 3: Graph x y 2 8 1 1 0 4 1 1 2 8 Section 6.7 2 y = – 3x + 4 Axis: x = 0 Vertex: (0, 4) Notice that the sign of the coefficient of the squared term indicates the direction of the parabola: If a > 0, the parabola opens upward. If a < 0, the parabola opens downward. Also notice that the constant is the y-intercept when the equation is written in standard form: 2 y = ax + bx + c By looking at the graph of a quadratic equation, which is a parabola, we can see that quadratic equations 2 are functions. Each x-value has one and only one y-value. Instead of writing y = ax + bx + c, we can also 2 write f(x) = ax + bx + c. Graphing a quadratic function is the same as graphing a quadratic equation. V. Zabrocki page 2