Solving Quadratic Equation by Graphing

Quadratic Equation y = ax2 + bx + c ax2 is the quadratic term. bx is the linear term. c is the constant term. The highest exponent is two; therefore, the degree is two.

Identifying Terms Example f(x)=5x2-7x+1 Quadratic term 5x2 Linear term -7x Constant term 1

Identifying Terms Example f(x) = 4x2 - 3 Quadratic term 4x2 Linear term 0 Constant term -3

Identifying Terms Now you try this problem. f(x) = 5x2 - 2x + 3 quadratic term linear term constant term 5x2 -2x 3

Quadratic Solutions The number of real solutions is at most two. • • • No solutions One solution Two 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.

Identifying Solutions Example f(x) = x2 - 4 Solutions are -2 and 2.

Identifying Solutions Now you try this problem. f(x) = 2x - x2 Solutions are 0 and 2.

Graphing Quadratic Equations 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 = x2 - 4x Roots 0 and 4 , Vertex (2, -4) , Axis of Symmetry x = 2 x y 1 -3 2 -4 3 4

Graphing Quadratic Equations Try this problem y = x2 - 2x - 8. Roots Vertex Axis of Symmetry x y -2 -1 1 3 4

Graphing Quadratic Equations The graphing calculator is also a helpful tool for graphing quadratic equations. Refer to classwork1 for directions for graphing quadratic equations on the Casio.