Name:__________ warm-up 4-2 Does the function f(x) = 3x 2 + 6x have a maximum or a minimum value? Find the y-intercept of f(x) = 3x 2 + 6x Find the equation.

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Name:__________ warm-up 4-2 Does the function f(x) = 3x 2 + 6x have a maximum or a minimum value? Find the y-intercept of f(x) = 3x 2 + 6x Find the equation of the axis of symmetry for f(x) = 3x 2 + 6x. Find the x-coordinate of the vertex of the graph of the function f(x) = 3x 2 + 6x.

Graph f(x) = 3x 2 + 6x. Which parabola has its vertex at (1, 0)? A.y = 2x 2 – 4x + 3 B.y = –x 2 + 2x – 1 C.y = x 2 + x + 1 D.y = 3x 2 – 6x

Details of the Day EQ: How do quadratic relations model real-world problems and their solutions? Depending on the situation, why is one method for solving a quadratic equation more beneficial than another? How do transformations help you to graph all functions? Why do we need another number set? I will be able to… Activities: Warm-up Review homework Notes: Solving quadratics by Graphing Retest-chapter one Class work/ HW Vocabulary: quadratic equation standard form root zero. Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing.

4-2 Solving Equations by Graphing Graphing QuadraticsQuadraticsQuadraticsQuadraticsQuadraticsQuadraticsQuadraticsQuadraticsQuadratic sQuadratics QuadraticsQuadraticsQuadraticsQuadraticsQuadratics GraphingGraphingGraphingGraphingGraphi GraphingGraphingGraphingGraphingGraphingi GraphingGraphingGraphingGraphingGraphinging

A Quick Review Does the function f(x) = 3x 2 + 6x have a maximum or a minimum value? Find the y-intercept of f(x) = 3x 2 + 6x Find the equation of the axis of symmetry for f(x) = 3x 2 + 6x. Find the x-coordinate of the vertex of the graph of the function f(x) = 3x 2 + 6x.

A Quick Review Graph f(x) = 3x 2 + 6x. Which parabola has its vertex at (1, 0)? A.y = 2x 2 – 4x + 3 B.y = –x 2 + 2x – 1 C.y = x 2 + x + 1 D.y = 3x 2 – 6x

Notes and examples Solve x 2 + 6x + 8 = 0 by graphing Solve x 2 + 2x – 3 = 0 by graphing

Notes and examples

Use a quadratic equation to find two numbers with a sum of 4 and a product of 5. Let x = one of the numbers. Then 4 – x = the other number. Plan (The product of the two numbers is 5) Graph the related function

Notes and examples NUMBER THEORY Use a quadratic equation to find two numbers with a sum of 7 and a product of 14.

Notes and examples Solve x 2 – 4x + 2 = 0 by graphing. What are the consecutive integers between which the roots are located?

Notes and examples HOOVER DAM One of the largest dams in the United States is the Hoover Dam on the Colorado River, which was built during the Great Depression. The dam is feet tall. Suppose a marble is dropped over the railing from a height of 6 feet above the top of the dam. How long will it take the marble to reach the surface of the water, assuming there is no air resistance? Use the formula h(t) = –16t 2 + h 0, where t is the time in seconds and h 0 is the initial height above the water in feet.