Homework LogTues

11/17

Lesson 4 – 1

Learning Objective: To find difference quotients & to graph functions

Hw: #401 Pg. 220 #1 – 8 all, 37 – 49 odd

11/17/15 Lesson 4 – 1 Distance Formula & Parabolas Day 1

Advanced Math/Trig

Learning Objective

To find distance between two points

To graph parabolas

Distance Formula

Distance d between two pts (, ) & (, )

1. (–1, 3) & (7, –3)

Distance Formula2. Find the shortest distance between (4, 3) and the line x = –5.

Find the distance between (4, 3) and (– 5, 3)

Is the perpendicular line drawn from the point to the given line(4, 3)

x = –5

(–5, 3)

= = 9

Quadratic Function Graph is an up/down parabola

Vertex Form

Vertex: (h, k)

Axis of Symmetry: x = h

Standard Form

y

Vertex:

Axis of Symmetry:

Quadratic Function Graph is a sideways parabola

Vertex Form

Vertex: (h, k)

Axis of Symmetry: y = k

Standard Form

x

Vertex:

Axis of Symmetry:

Quadratic Function If a > 0 (positive)

Opens up or RIGHT

If a < 0 (negative)

Opens down or LEFT

Graph3. a = –2 Opens leftVertex: (3, 1) AoS: y = 1

x y

–5 1

–10

1 –5

23

V( 3 1)

Graph4. a = –1 Opens left = Vertex: (4, 3) AoS: y = 3

x y

0 3

12

3 0

45

V( 4 3)

Graph5. Get rad alone: Square both sides: Solve for x: a = 1, opens rightVertex (2, 1)

x y

X X

–10

3 6

23

V( 2 1)

Graph6. Get rad alone: Square both sides: Solve for x: a = 1, opens rightVertex (2, 1)

x y

6 3

–10

X X

23

V( 2 1)

Graph7. xSquare both sides: Solve for x: a = 1, opens up = Vertex (0, 3)

x y

–2 –1

XX

1 2

47

V( 0 3)

Graph8. Write an equation of the parabolaOpens up with V(1, –4)Pick either of the other pts(3, 0) 4 = 4a a = 1 V(1, –4)

(3, 0)(–1, 0)

Graph9. Write an equation of the parabolaOpens left with V(4, 3)Pick either of the other pts(0, 1) –4 = 4a a = – 1

V(4, 3)

(0, 5)

(0, 1)

Ticket Out the Door

Graph

Explain WHY your graph makes sense

Homework

#401 Pg. 220 #1 – 8 all, 37 – 49 odd