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# Solving quadratics by graphing notes

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### Solving quadratics by graphing notes

1. 1. Solving Quadratic Equations by Graphing
2. 2. Quadratic Equationy = ax2 + bx + c 2ax is the quadratic term.bx is the linear term.c is the constant term.The highest exponent is two; therefore, the degree is two.
3. 3. Quadratic Solutions The number of real solutions is at most two. 6 f( ( ⋅ x ) x 2 -2 x ) = +5 6 2 4 4 2 -5 5 2 -2 5 5 -4 -2 -2 No solutions One solution Two solutions
4. 4. Solving EquationsWhen 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.
5. 5. Identifying Solutions 2 4 Example f(x) = x - 4 2 -5 -2 -4 Solutions are -2 and 2.
6. 6. Identifying Solutions Now you try this problem. 4 2 f(x) = 2x - x 2 5 -2 Solutions are 0 and 2. -4
7. 7. 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.
8. 8. Graphing Quadratic Equations One method of graphing uses a table with arbitrary x-values. 4 Graph y = x2 - 4x 2 x y 0 0 5 1 -3 2 -4 -2 3 -3 4 0 -4 Roots 0 and 4 , Vertex (2, -4) , Axis of Symmetry x = 2