Warmup Does the function f(x) = 3x2 + 6x have a maximum or a minimum value?

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Presentation transcript:

warmup Does the function f(x) = 3x2 + 6x have a maximum or a minimum value?

4-2 Solving Quadratic equations by graphing Goal: Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing.

A quadratic equation in the form ax2 + bx + c = 0 has a related function f(x) = ax2 + bx + c. The zeros of the function are the x-intercepts of its graph. These x-values are the solutions or roots of the related quadratic equation. A quadratic equation can have one real solution, two real solutions, or no real solutions. Finding the x-intercepts (roots) from a graph without the use of a graphing calculator usually provides a rather imprecise estimate of the solutions. Solutions that appear to be integers can be verified by substituting them into the original equation.

Use the related graph of the equation to determine its solutions

Use the related graph of the equation to determine its solutions

Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.

NUMBER THEORY Use a quadratic equation to find two numbers with a sum of 4 and a product of 5. Understand Let x = one of the numbers. Then 4 – x = the other number. Plan x(4 – x) = 5 The product is 5. 4x – x2 = 5 Distributive Property x2 – 4x + 5 = 0 Add x2 and subtract 4x from each side. Solve Graph the related function.

Problems from p. 237, Solving quadratic equation by graphing: Solve each equation. Round to the nearest tenth if necessary.