Section 3.1 Day 3 – Quadratic Functions After this section you should be able to: Solve real-world problems using quadratic functions.

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Section 3.1 Day 3 – Quadratic Functions After this section you should be able to: Solve real-world problems using quadratic functions.

Given real-world applications, we won’t always be able to find the standard form of every quadratic function. There is an alternate method to finding the vertex of a quadratic function. Also, if you are able to use your graphing calculator, you can find the vertex using the max/min features. Find the vertex of this quadratic function.

1. Enter the quadratic function into y = Using your graphing calculator to find the vertex 2. Press GRAPH to view the parabola 3. Press 2 nd TRACE (CALC) select minimum or maximum 4. Place the cursor to the left and to the right of the min/max area pressing enter each time 5. Press enter one more time for the “guess” 6. The x and y – coordinates of the vertex are given to you. Use your graphing calculator to find the vertex of this quadratic function: *you may need to adjust your WNDOW

1. If the path of a baseball is represented by the function: The maximum height of the baseball is ft. The maximum occurs when x = ft from home plate. Solve real-world problems using quadratic functions. where f(x) is the height of the baseball (in feet), and x is the horizontal distance from home plate (in feet) Find the maximum height reached by the baseball. *You may need to adjust the window in order to see the entire curve.

2. Given the perimeter of a rectangular area is 46 meters: The maximum area of the rectangle is meters. The maximum occurs when x = 11.5 meters, so y = 11.5 meters. Solve real-world problems using quadratic functions. a. Express the area A as a function of x and determine it’s domain. *What values can x be? b. Find the length and width of the rectangle that will maximize the area. x x y y Let x be the length y be the width Solve for y length cannot = 0 so x ≠ 0 width cannot = 0 so x ≠ 23 The Domain is (0 < x < 23) Both the width and the length must be 11.5 meters in order to maximize the area.

YOU TRY: 1. Find two positive real numbers whose product is a maximum and sum is 110. The maximum value of the quadratic function is The maximum occurs when x = 55. When x = 55, then y = 55. The two numbers are 55 and 55 Solve real-world problems using quadratic functions.

You Try: 2. The perimeter of a rectangle is 200 meters. Find the dimensions of the rectangle with the maximum area. The maximum area is The maximum area occurs with dimensions 50 x 50. Solve real-world problems using quadratic functions.

ACT RESULTS Areas I did wellAreas where I need work My Personal ACT Goal is:

Section 3.1 Day 3 – Quadratic Functions After this section you should be able to: Homework: Pg. 260 #75, 76, 77cd, 85, 87 ACT practice #1 Solve real-world problems using quadratic functions.