Trig Lab Worksheets

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Math 1083 Worksheet 22 Getting Ready for the Parabola Objectives:

1. Review transformation

2. Review completing the squares

3. Solve systems of equations

Open the link https://www.geogebra.org/m/P63pwtxg. Use the applet to review how to graph a

function using transformation.

#1 The graph of 𝑓(𝑥) = 𝑥2 is given. Graph the following functions on the same coordinates.

a) Graph 𝑔(𝑥) = 𝑓(𝑥 − 2)

b) Graph ℎ(𝑥) = 𝑓(𝑥 + 1) − 2

c) Graph 𝑘(𝑥) = −𝑓(𝑥 − 2)

a) Graph 𝑔(𝑥) = 𝑓(𝑥) + 1

b) Graph ℎ(𝑥) = 𝑓(𝑥 − 2) + 1

c) Graph 𝑘(𝑥) = −𝑓(𝑥) + 1

#2 Using transformation, give the equation of each graph. Write the answer of the form 𝑦 =

𝑎(𝑥 − ℎ)2 + 𝑘 𝑜𝑟 𝑥 = 𝑎(𝑦 − 𝑘)2 + ℎ

a)

b)

c)

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#3 Graph the parabola from the given information. Then write the equation.

a) Vertex (2, –3) b) Vertex (–1, –3)

Passing (1, –2) and (4, 1) passing (3, –1) and y-int (0, −4)

#4 Complete the squares.

a) 𝑥2 + 4𝑥 − 𝑦 − 12 = 0 for x b) 2𝑥 + 𝑦2 − 6𝑦 = 1 for 𝑦

#5 Solve the system of equations

a) { 𝑥 − 𝑦 = 11

2𝑥 + 𝑦 = 19 b) {

−3𝑥 − 2𝑦 = 1 6𝑥 + 4𝑦 = −2