Dispatch 4 Solving Quadratic Equations by Graphing Standard

Dispatch 4

Solving Quadratic Equations by Graphing Standard: 21. 0

Let’s Review Vocabulary Roots vertex maximum Equation parabola y r t e m m y S f o Line Minimum x-intercept y-intercept

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.

Solving Equations • When we talk about solving these equations, we want to find the value of x when y = 0. These values, are where the graph crosses the x-axis, are called the xintercepts. • These values are also referred to as solutions, zeros, or roots.

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

Identifying Solutions 2 Example x – 4 = 0 Solutions are -2 and 2.

Identifying Solutions – x 2 + 6 x – 9 = 0 Solution is 3.

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

Identifying Solutions x 2 + 4 x + 8 = 0 No solution.

Graphing Quadratic Equations One method of graphing uses a table with arbitrary x-values. Graph y = x 2 - 4 x x y 0 1 2 3 4 0 -3 -4 -3 0 Roots 0 and 4 , Vertex (2, -4) , Axis of Symmetry x = 2

Graphing Quadratic Equations Try this problem x 2 - 2 x – 8 = 0. x y -2 -1 1 3 4 Roots Vertex Axis of Symmetry

Italy and Jorge like playing soccer. If they kicked the ball represented by the equation x 2 + 6 x = 7, can you them solve the equation by graphing.