Solving Quadratic Equation by Graphing Section 6.1
Quadratic Equation y = ax 2 + bx + c ax 2 is the quadratic term. bx is the linear term. c is the constant term. The highest exponent is two; therefore, the degree is two.
Example f(x)=5x 2 -7x+1 Quadratic term 5x 2 Linear term -7x Constant term 1 Identifying Terms
Example f(x) = 4x 2 - 3 Quadratic term 4x 2 Linear term 0 Constant term -3 Identifying Terms
Now you try this problem. f(x) = 5x 2 - 2x + 3 quadratic term linear term constant term Identifying Terms 5x 2 -2x 3
The number of real solutions is at most two. Quadratic Solutions No solutionsOne solutionTwo solutions
Solving Equations When we talk about solving these equations, we want to find the value of x when y = 0. These values, where the graph crosses the x-axis, are called the x-intercepts. These values are also referred to as solutions, zeros, or roots.
Example f(x) = x 2 - 4 Identifying Solutions Solutions are -2 and 2.
Now you try this problem. f(x) = 2x - x 2 Solutions are 0 and 2. Identifying Solutions
The graph of a quadratic equation is a parabola. The roots or zeros are the x-intercepts. The vertex is the maximum or minimum point. All parabolas have an axis of symmetry. Graphing Quadratic Equations
One method of graphing uses a table with arbitrary x-values. Graph y = x 2 - 4x Roots 0 and 4, Vertex (2, -4), Axis of Symmetry x = 2 Graphing Quadratic Equations xy 00 1-3 2-4 3-3 40
Try this problem y = x 2 - 2x - 8. Roots Vertex Axis of Symmetry Graphing Quadratic Equations xy -2 1 3 4
The graphing calculator is also a helpful tool for graphing quadratic equations. Refer to classwork1 for directions for graphing quadratic equations on the Casio. Graphing Quadratic Equations