1 A baseball is hit at a point 3 feet above the ground at a velocity of 100 feet per second and at an angle of 45  with respect to the ground. The path of the baseball is given by the function f (x) = –0.0032x 2 + x + 3, where f (x) is the height of the baseball (in feet) and x is the horizontal distance from home plate (in feet). What is the maximum height reached by the baseball? Do Now– The Maximum Height of a Projectile

Copyright © Cengage Learning. All rights reserved. Pre-Calc Honors 2.1: Quadratic Functions HW: p (10-22 even, 64, 66) HW tomorrow: p (32-40 even, 46, 50, 52, 60, 68)

3 Copyright © Cengage Learning. All rights reserved. Pre-Calc Honors 2.1: Quadratic Functions HW: p (32-40 even, 46, 50, 52, 60, 68)

4 Polynomial Functions

5 Polynomial functions are classified by degree. 1.) f (x) = a, a  0, has degree = ___ and is called a ________ function. Graph looks like: _______________ 2.) f (x) = mx + b, m  0 has degree = ___ and is called a ________ function. Graph looks like: _______________ 3.) f (x) = ax 2 + bx + c, a  0 has degree = ___ and is called a ________ function. Graph looks like: _______________

6 The Basic Characteristics of a Quadratic Function Quadratics can be presented in the following forms: f(x) = ax 2 + bx + c f(x) = a(x – h) 2 + k f(x) = a(x – p)(x – q) Basic Characteristics: Shape of a quadratic is a ________________. Opens up when __________ and down when __________. Domain:,Range: Axis of symmetry is a __________ line going through the ___________. The vertex is also a maximum or minimum of the function depending on if it opens up or down. Find x-int by _____________ and y-int by _____________.

7 The Standard Form of a Quadratic Function In Algebra II, we call this vertex form and Standard form is f(x) = ax 2 + bx + c.

8 Graph quadratic functions by hand. 1.) f(x) = a(x – h) 2 + k 2.) f(x) = a(x – p)(x – q) 3.) f(x) = ax 2 + bx + c

9 Graph the quadratic function. Graph the function. Label the vertex, x-intercept, y-intercept, and axis of symmetry. Determine the domain and range. 1.) 2.) 3.)

10 Write an equation. Write an equation of the parabola in standard form. 1.) Vertex: (-2, 5), passes through (0, 9). 2.) Vertex: (-1, 4), x-intercepts: -3 and 1.

11 Maximizing a product of two numbers. Find the two positive real numbers with a sum of 110 whose product is a maximum.

12 p.98 #67 To make a sign holder, you bend a 100-inch long steel wire x inches from each end to form two right angles. To use the sign holder, you insert each end 6 inches into the ground. a.) Write a function for the rectangular area A enclosed by the sign holder in terms of x. b.) Determine the value of x that maximizes the rectangular area.