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Solving Quadratic Equations by Graphing Standard: 21.0

Let’s Review Vocabulary Roots Equation vertex parabola maximum Line of Symmetry 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 x-intercepts. These values are also referred to as solutions, zeros, or roots.

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

Identifying Solutions Example x2 – 4 = 0 Solutions are -2 and 2.

Identifying Solutions – x2 + 6x – 9 = 0 Solution is 3.

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

Identifying Solutions x2 + 4x + 8 = 0 No solution.

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 x2 - 2x – 8 = 0. Roots Vertex Axis of Symmetry x y -2 -1 1 3 4

Italy and Jorge like playing soccer Italy and Jorge like playing soccer. If they kicked the ball represented by the equation x2 + 6x = 7, can you them solve the equation by graphing.