Solving quadratics by graphing notes
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This document discusses solving quadratic equations by graphing. It explains that a quadratic equation has the form y=ax^2 + bx + c, with the quadratic, linear, and constant terms. A quadratic equation will have 0, 1, or 2 real solutions depending on the graph. The solutions are the x-intercepts where the graph crosses the x-axis. Examples show how to identify the solutions by graphing and finding the x-intercepts. The graph of a quadratic is a parabola with roots/zeros at the x-intercepts and a vertex as its maximum or minimum point. One method for graphing uses a table to plot points and sketch the parabola.
Solving quadratics by graphing notes
- 1. Solving Quadratic Equations by Graphing
- 2. Quadratic Equation y = ax2 + bx + c 2 ax 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. 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. 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.
- 5. Identifying Solutions 2 4 Example f(x) = x - 4 2 -5 -2 -4 Solutions are -2 and 2.
- 6. Identifying Solutions Now you try this problem. 4 2 f(x) = 2x - x 2 5 -2 Solutions are 0 and 2. -4
- 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. 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