Solving Quadratic Equations by Graphing 4 Lesson 10.2

4 The number of real solutions is at most two. Quadratic Solutions No solutionsOne solutionTwo solutions

Solving Equations 4 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. 4 These values are also referred to as solutions, zeros, or roots.

4 Example y = x Identifying Solutions Solutions are -2 and 2.

4 Now you try this problem. l y = 2x - x 2 4 Solutions are 0 and 2. Identifying Solutions

4 The graph of a quadratic equation is a parabola. 4 The roots or zeros are the x- intercepts. 4 The vertex is the maximum or minimum point. 4 All parabolas have an axis of symmetry. Graphing Quadratic Equations

4 One method of graphing uses a table with x values. 4 Graph y = x 2 - 4x 4 Find the axis of symmetry 1 st : -b 4 2a 4 Substitute the x = (a.o.s) into the equation, 4 solve for y. 4 This creates the ordered pair for the vertex. 4 Pick 2 x’s on each side of the vertex point to find 4 more points to graph the parabola. 4 The root(s) or solution(s) are where 4 the graph intercepts the x-axis.  Axis of Symmetry x = 2Vertex (2, -4) 4 Roots 0 and 4 4 Graphing Quadratic Equations

4 The graphing calculator is also a helpful tool for graphing quadratic equations. 4 Enter the equation into the graphing calculator. 4 Graph to see how many roots the equation has. 4 2 nd Calc Zero to find each root.  ebra1/Quadratic1.htm (1 and 3) ebra1/Quadratic1.htm 4 You can also solve for the roots by factoring. Graphing Quadratic Equations