3.1 Quadratic Functions

Polynomials- classified by degree (highest exponent)

• Degree:• 0 - constant function- horizontal line• 1 - linear function- • 2 - quadratic function-

(parabola, vertex, axis of symmetry, opens up or down…)

baxxfbmxxf /

cbxaxxf 2

Vertex Form

is the axis of symmetry

is the vertex

If a >0, the parabola opens up

If a <0, the parabola opens down

khxaxf 2

hx

kh,

Writing the Equation of a Parabola in Vertex Form

782 2 xxxf

862 xxxf

Vertex of a Parabola

If , then the x coordinate of the vertex of the parabola isSo the vertex is:

cbxaxxf 2

a

bx

2

,2 2

b bf

a a

Write the standard form of the equation of the parabola whose vertex is (1, 2) and passes through (0, 0).

Application

A baseball is hit at a point 3 feet above the ground at a velocity of 100 feet per second at an angle of 45 degrees with respect to the ground. The path of the baseball is given by the function

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?

2( ) 0.0032 3f x x x