Post on 02-Jan-2016
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