LESSON 6 3 Creating and Comparing Quadratics REVIEW

LESSON 6. 3 Creating and Comparing Quadratics

REVIEW Quadratic Equations � Degree � Graph of 2. is a parabola. � Standard � Vertex form: f(x) = ax 2 + bx + c f(x) = a(x – h)2 + k

EXAMPLE 1: CREATE AN EQUATION x -4 -3 -2 -1 0 1 2 3 4 y -3 -6 -7 -6 -3 2 9 18 29

EXAMPLE 2: CREATE AN EQUATION

EXAMPLE 3: CREATE AN EQUATION Vertex (1, 12) Point on the graph (4, -6)

YOUR TURN Write an equation for the situation. X -4 -3 -2 -1 0 1 2 3 4 F(x) 112 79 52 31 16 7 4 7 16

LESSON 6. 3 CONT.

WHY DO WE NEED TO KNOW THIS? Quadratics model the distance something has fallen because of the acceleration of gravity. General Formula (Height in feet in terms of time) h(t) = -16 t 2 + vt + h Height of the object after time, t. • Initial velocity • If thrown up, v is positive. • If thrown down, v is negative Initial height

General Formula (Height in meters in terms of time) h(t) = -4. 9 t 2 + vt + h

EXAMPLE 4: You are standing on a platform 300 ft in the air and throw a ball straight up at 20 ft/s. Write an equation to represent the height of the ball in terms of time when you threw the ball. Your friend is standing on a different platform 200 ft in the air and throws a ball straight up at 40 ft/s. Write an equation to represent the height of the ball in terms of time when your friend threw the ball.

EXAMPLE 4 CONT. When did your ball reach its maximum height? What was it? When did your friend’s ball reach its maximum height? What was it? When did your ball hit the ground? When did your friend’s ball hit the ground?

HOMEWORK Worksheet 6. 3 #1 – 3, 6 – 12