Quadratic Functions – Maximum and Minimum Word Problems 1. Projectile Motion  Maximum Height 2. Numbers  Maximizing or Minimizing number combinations 3. Maximizing Area 4. Maximizing Revenue

Teach With Fergy Preview File Please enjoy this preview of your Power Point. Bolded words are blank on student notes, they are filled in during the lesson Some slides appear blank because they have been removed. Other slides may have ........... on them, this represents writing that has been removed. Please note that the Entire Unit Package can also be purchased at a steep discount from my Store.

Day 1 There are 4 types of maximum/minimum word problems: 1. Projectile Motion  Maximum Height 2. Numbers  Maximizing or Minimizing number combinations 3. Maximizing Area 4. Maximizing Revenue

Steps to solving Maximum and Minimum Word Problems Identify the quantity to be maximized or minimized and write an algebraic expression for this quantity. Rewrite the expression using only 1 variable (ie. "x”) ……………… Expand and simplify to change the second equation into standard form. y = ax2 + bx + c Complete the square to maximize / minimize the function. y = a(x – h)2 + k Make a maximum / minimum statement to fully answer the question.

Type 1: Projectiles Example 1: A football is kicked so that its height, h meters after t seconds is given by the expression: h = 22t - 5t2. a) What is the height of the Football when it is kicked? When the football is kicked, t = ………………   h = 22t - 5t2 h = 22(0) - 5(0)² h = 0 The height of the football when it is kicked ………………

b) What is the maximum height of the football? h = 22t - 5t2 h = - 5t2 + 22t ……………… h = -5[t2 - 4.4t + 4.84 – 4.84] h = -5(t - 2.2)2 + 24.2 The maximum height is 24.2 m above the ground

c) When does the football reach its maximum height? h = 24.2 ………………   The ball reaches its maximum height 2.2 seconds after it is kicked

d) Sketch the graph. The vertex of the football’s path is (2.2, 24.2) One x-intercept is (0, 0) because that’s time = 0 Since the axis of symmetry is x = 2.2, the other x-intercept is 2.2 + 2.2 = 4.4 or set h = 0 0 = -5(t - 2.2)2 + 24.2 -24.2/-5 = (t-2.2)2 ………………

e) How long is the ball in the air? Since graph is symmetrical about its axis of symmetry, x= 2.2, and the ball is on the ground when t = 0, it will hit the ground again when ……………… Or think of it like this, it will take an object the same amount of time to go up as come down.

Type 2: Numbers Example 1: The sum of two numbers is twelve. Find the numbers and the maximum of their product. Step 1. Assign the variables ……………… Let y represent the second number.   Step 2. Write the info in terms of only one variable (x). Since the sum of the two numbers is twelve: x + y = 12 12 – x = y y = 12- x

The remaining 19 slides have been removed The remaining 19 slides have been removed. Below see what the student notes look like.