Unit 5: Graphing Quadratics Review



UNIT 5 REVIEW: GRAPHING QUADRATIC RELATIONS

TERMINOLOGY

STANDARD FORM FACTORED FORM VERTEX FORM

[pic] y = a(x – s)(x – t) y = a(x – h)2 + k

For the Unit Test, you should be able to do each of the following:

• identify each part of the parabola given corresponding forms (ie. identify the zeros from factored form; identify vertex from vertex form; identify y-intercept from standard form; identify direction of opening; identify axis of symmetry; identify optimum value and whether the optimum value is a maximum or minimum, etc.)

• expand both factored form and vertex form to get Standard Form.

• factor to get factored form

• complete the square to get vertex form.

• find the vertex from factored form (last unit)

• find the equation of the parabola using vertex form if you know the vertex and one point:

→ Sub in vertex (h and k) and the point (x and y) and solve for a

→ Write the equation replacing variables a, h and k with values

TRANSFORMATIONS

• The base curve is: y = x2

• The new curve is:

[pic]

• You should be able to describe transformations

• You should be able to write the new equation if given transformation descriptions

• You should be able to graph using transformations

→ Draw the base curve first

→ Stretch or compress

→ Reflect in the x-axis

→ Move left/right

→ Move up/down

→ Show all graphs needed to get to your final parabola. Full marks will only be given if the transition graphs are shown. Clearly label all graphs.

REVIEW (in addition to textbook question)

1. Describe the transformations to y = x2 and graph each of the following using transformations.

a. y = (x – 1)2 – 4

b. y = 2(x + 3)2 + 1

c. y = ¼ (x – 5)2 + 1

d. y = – (x + 2)2 + 6

2. Expand each of the following to change factored form to standard form.

a. y = (x + 3)(x – 5)

b. y = 3(x – 5)(x + 6)

c. y = – 2 (x – 7)(x – 9)

3. Identify the vertex in each of the following and then expand each to change vertex form to standard form.

a. y = (x + 3)2 – 10

b. y = 3(x +15)2 – 625

c. y = –7(x – 7)2 + 4

4. Factor each of the following to change standard form to factored form. Identify the zeros of each parabola and use the zeros to find the vertex of the parabola.

a. y = x2 – 8x + 15

b. y = 2x2 + 6x – 20

c. y = –3x2 + 6x + 24

5. Complete the square on each of the following to change standard form to vertex form. Identify the optimum value and state the axis of symmetry.

a. y = x2 + 8x + 5

b. y = 2x2 + 12x +11

c. y = –5x2 + 10x + 3

6. Find the equation of the parabola that has vertex (–5, –1) and passes through (–4, 2).

Also, Textbook work on page 431 # 7, 8

-----------------------

axis of

symmetry

zero, root, x-intercept

zero, root, x-intercept

vertex

y-coordinate is the optimum value

x-coordinate

is the axis of symmetry

If [pic], reflection in x-axis

If [pic] or [pic], vertical stretch

by a factor of a

If[pic], vertical compression by

a factor of 1/a

If [pic], translation up

k units.

If [pic], translation down

k units.

If [pic], translation right

h units.

If [pic], translation left

h units.

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