§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.

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§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.

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§6.2 Solving Quadratic Equations by Graphing

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§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:

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§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:

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§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.

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§6.2 Solving Quadratic Equations by Graphing Estimate Roots (Solutions) Axis of symmetry: Solutions: and

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§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.

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§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

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§6.2 Solving Quadratic Equations by Graphing

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