Chapter 2: Quadratic Functions

The ________ is c; the point (0, c) is on the parabola.

________- a line that divides a parabola into mirror images and passes through the vertex; the ________ is the vertical line x= h or x=- b /2a.

For the ________ f (x)= ax2 + bx + c, the y- coordinate of the vertex is the minimum value of the function when a> 0 and the maximum value when a <0.

Transformations of Quadratic Functions

h)2 + k, where a ≠ 0

h)2 + k, where a ≠ 0 and the vertex is (h, k)

Characteristics of Quadratic Functions

a line that divides a parabola into mirror images and passes through the vertex; the axis of symmetry is the vertical line x = h or x = -b/2a

a quadratic function written in the form f(x) = ax2 + bx + c

f(-b/2a)

all real numbers

y ≥ f(-b/2a)

f(-b/2a)

all real numbers

y ≤ f(-b/2a)

Modeling with Quadratic Equations

a function that can be written in the form f(x) = a(x - h)2 + k, where a ≠ 0

the U-shaped graph of a quadratic function

the lowest part on a parabola that opens up or the highest point on a parabola that opens down

f(x) = a(x - h)2 + k, where a ≠ 0 and the vertex is (h, k)

a line that divides a parabola into mirror images and passes through the vertex; the axis of symmetry is the vertical line x = h or x = -b/2a

a quadratic function written in the form f(x) = ax2 + bx + c

a quadratic function in the form f(x) = a(x - p)(x - q)

the y-coordinate of the vertex when a > 0

the y-coordinate of the vertex when a < 0