Quadratics Lab P. 6

VI. Further investigations in the parabola: 1. The general form y = a(x-h)2 + k Graph each parabola and complete the table below: Parabola y=x2-5

a

h

k

Axis of Symmetry

Vertex

(h,k)

y=-2(x-l) 2 -5

y = 4(x + 3)2 - 2 y = .5(x-4)2+ 1 y = -(2/3)(x+ I)2 -3

Using the information provided above, given the equation of a parabola in the form y = a(x-h)2 + k what is the vertex and the axis of symmetry? Vertex

Axis of Symmetry

The variable a serves the same purpose in all forms of a parabola. What happens in the parabola if a is positive

if a is negative

Is the parabola wide or narrow in comparison to a parabola where a = 1 if la I is a large number

if lal is a small number

Write an equation of a parabola satisfying the following conditions: a.) Axis of symmetry, x = -2

Vertex (-2,7)

Opens up

a.)

b.)

b.) Axis of symmetry x = 5

Vertex (5,-3)

Opens down

c.) Axis of symmetry x = 0

Vertex (0,-3)

Opens upand is wide

d.) Axis of symmetry x =-3

Vertex (-3, 4)

Opens down and is narrow

d.)