Solving Quadratic Equations by Graphing

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Information about Solving Quadratic Equations by Graphing
Education

Published on March 31, 2008

Author: rfantster

Source: authorstream.com

Slide1:  §6.2 Solving Quadratic Equations by Graphing 1) quadratic equation 2) root 3) zero Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing. Slide2:  §6.2 Solving Quadratic Equations by Graphing When a quadratic function is set equal to a value, the result is a quadratic equation. The solution of a quadratic equation are called the roots of the equation. One method for finding the roots of a quadratic equation is to find the zeros of the related quadratic function. The zeros of the function are the x-intercepts of its graph. These are the solutions of the related equation because f(x) = 0 at those points. The zeros of the function graphed at the right are -1 and 2. Slide3:  §6.2 Solving Quadratic Equations by Graphing Slide4:  §6.2 Solving Quadratic Equations by Graphing Two Real Solutions Axis of symmetry: Note: The parabola opens up and the vertex is below the x-axis. Therefore, the parabola must cross the x-axis at two distinct points. Solutions: Slide5:  §6.2 Solving Quadratic Equations by Graphing One Real Solution Axis of symmetry: Note: The parabola opens up and the vertex is on the x-axis. Therefore, the parabola only touches the x-axis at the vertex (1 point). Solution: Slide6:  §6.2 Solving Quadratic Equations by Graphing No Real Solution Axis of symmetry: Note: The parabola opens down and the vertex is below the x-axis. Therefore, the parabola never crosses the x-axis. Solution: No REAL solution. Slide7:  §6.2 Solving Quadratic Equations by Graphing Estimate Roots (Solutions) Axis of symmetry: Solutions: and Slide8:  §6.2 Solving Quadratic Equations by Graphing Number Theory Use a quadratic equation to find two real numbers that satisfy the situation, or show that no such number exists. Axis of symmetry: Solution: No REAL solution. Slide9:  §6.2 Solving Quadratic Equations by Graphing Application of Physics A tennis ball is hit upward at a velocity of 48 feet per second. 3 seconds Slide10:  §6.2 Solving Quadratic Equations by Graphing

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