Example 6: (x + 2)(x - 7) = 5 3[(x + 2)(x - 7)] = 3[5] 1(x + 2)(x - 7) = 15 x - 5x - 14 = 15 2 x - 5x - 29 = 0 2 a = 1 b = -5 c = -29 Remember, to be a quadratic equation, the integers a, b, and c must have a greatest common factor of 1. Example 7: x - 2x + 1 = 0 is not a quadratic equation because it contains a third-degree term. 3 2 Example 8: 3x - 11 = 0 is not a quadratic equation because it does not contain a second-degree term. In fact, you may recall that this is a linear equation. Solve Quadratic Equations Graphically The solution of the quadratic equation is the point or points on the graph where y is equal to zero, or the x-intercepts. If the parabola never crosses the x-axis, there is no solution to the equation. Example: The parabola shown is the graph of y = x - 4x + 5. 2 Find the solutions of the quadratic equation 0 = x - 4x + 5. 2 Solution: The solutions are the x-intercepts. The parabola does not cross the x-axis. There are no solutions to the quadratic equation. The solution set of 0 = x - 4x + 5 is Ø. 2
Example 6: (x + 2)(x - 7) = 5 3[(x + 2)(x - 7)] = 3[5] 1(x + 2)(x - 7) = 15 x 2 - 5x - 14 = 15 x 2 - 5x - 29 = 0 a = 1 b = -5 c = -29 Remember, to be a quadratic equation, the integers a, b, and c must have a greatest common factor of 1. Example 7: x 3 - 2x 2 + 1 = 0 is not a quadratic equation because it contains a third-degree term. Example 8: 3x - 11 = 0 is not a quadratic equation because it does not contain a second-degree term. In fact, you may recall that this is a linear equation. Solve Quadratic Equations Graphically The solution of the quadratic equation is the point or points on the graph where y is equal to zero, or the x-intercepts. If the parabola never crosses the x-axis, there is no solution to the equation. Example: The parabola shown is the graph of y = x 2 - 4x + 5. Find the solutions of the quadratic equation 0 = x 2 - 4x + 5. Solution: The solutions are the x-intercepts. The parabola does not cross the x-axis. There are no solutions to the quadratic equation. The solution set of 0 = x 2 - 4x + 5 is Ø.
algebra_1_unit_2_lesson_6_to_10_graphing_quadratic_functions.docx