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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) = –0.0032x2 + 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

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Pre-Calc Honors2.1: Quadratic Functions

HW: p.96-98 (10-22 even, 64, 66)HW tomorrow: p.96-97 (32-40 even, 46, 50,

52, 60, 68)

3Copyright © Cengage Learning. All rights reserved.

Pre-Calc Honors2.1: Quadratic Functions

HW: p.96-97 (32-40 even, 46, 50, 52, 60, 68)

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Polynomial Functions

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Polynomial FunctionsPolynomial 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) = ax2 + bx + c, a 0

has degree = ___ and is called a ________ function.

Graph looks like: _______________

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The Basic Characteristics of a Quadratic Function

Quadratics can be presented in the following forms:f(x) = ax2 + bx + cf(x) = a(x – h)2 + kf(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 _____________.

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The Standard Form of a Quadratic Function

In Algebra II, we call this vertex form andStandard form is f(x) = ax2 + bx + c.

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Graph quadratic functions by hand.1.) f(x) = a(x – h)2 + k

2.) f(x) = a(x – p)(x – q)

3.) f(x) = ax2 + bx + c

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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.) 212)( xxf

521)( xxxf

118)( 2 xxxf

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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.

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Maximizing a product of two numbers.

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

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p.98 #67To 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.