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# 6.2 solve quadratic equations by graphing

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### 6.2 solve quadratic equations by graphing

1. 1. Solving Quadratic Equation by Graphing <ul><li>Section 6.1 </li></ul>
2. 2. Quadratic Equation <ul><li>y = ax 2 + bx + c </li></ul><ul><li>ax 2 is the quadratic term. </li></ul><ul><li>bx is the linear term. </li></ul><ul><li>c is the constant term. </li></ul><ul><li>The highest exponent is two; therefore, the degree is two. </li></ul>
3. 3. <ul><li>Example f(x)=5x 2 -7x+1 </li></ul><ul><li>Quadratic term 5x 2 </li></ul><ul><li>Linear term -7x </li></ul><ul><li>Constant term 1 </li></ul>Identifying Terms
4. 4. <ul><li>Example f(x) = 4x 2 - 3 </li></ul><ul><li>Quadratic term 4x 2 </li></ul><ul><li>Linear term 0 </li></ul><ul><li>Constant term -3 </li></ul>Identifying Terms
5. 5. <ul><li>Now you try this problem. </li></ul><ul><li>f(x) = 5x 2 - 2x + 3 </li></ul><ul><li>quadratic term </li></ul><ul><li>linear term </li></ul><ul><li>constant term </li></ul>Identifying Terms 5x 2 -2x 3
6. 6. <ul><li>The number of real solutions is at most two. </li></ul>Quadratic Solutions No solutions One solution Two solutions
7. 7. Solving Equations <ul><li>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. </li></ul><ul><li>These values are also referred to as solutions, zeros, or roots. </li></ul>
8. 8. <ul><li>Example f(x) = x 2 - 4 </li></ul>Identifying Solutions Solutions are -2 and 2.
9. 9. <ul><li>Now you try this problem. </li></ul><ul><li>f(x) = 2x - x 2 </li></ul><ul><li>Solutions are 0 and 2. </li></ul>Identifying Solutions
10. 10. <ul><li>The graph of a quadratic equation is a parabola. </li></ul><ul><li>The roots or zeros are the x-intercepts. </li></ul><ul><li>The vertex is the maximum or minimum point. </li></ul><ul><li>All parabolas have an axis of symmetry. </li></ul>Graphing Quadratic Equations
11. 11. <ul><li>One method of graphing uses a table with arbitrary </li></ul><ul><li>x-values. </li></ul><ul><li>Graph y = x 2 - 4x </li></ul><ul><li>Roots 0 and 4 , Vertex (2, -4) , </li></ul><ul><li>Axis of Symmetry x = 2 </li></ul>Graphing Quadratic Equations x y 0 0 1 -3 2 -4 3 -3 4 0
12. 12. <ul><li>Try this problem y = x 2 - 2x - 8. </li></ul><ul><li>Roots </li></ul><ul><li>Vertex </li></ul><ul><li>Axis of Symmetry </li></ul>Graphing Quadratic Equations x y -2 -1 1 3 4
13. 13. <ul><li>The graphing calculator is also a helpful tool for graphing quadratic equations. </li></ul>Graphing Quadratic Equations