Solving Quadratic Equations by Graphing

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.

Quadratic Solutions The number of real solutions is at most two. 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.

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

Identifying Solutions Now you try this problem. f(x) = 2x - x 2 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 = x 2 - 4x Roots 0 and 4, Vertex (2, -4), Axis of Symmetry x = 2 xy