Advanced Algebra Semester 1 Final Exam Review

steps to find the MAD

1) find the mean of the data set; 2) subtract to find the distance each value is from the mean; 3) find the mean of the distances (divide the sum of the distances by the number of values)

Second Quartile (Q2)

50th percentile (median) - middle of the data

Compression of f(x) = x² wider than the graph of f(x) = x²

Describe how the graph of g(x) = (1/5)x² is related to the graph f(x) = x²

Stretch of f(x) = x² narrower than the graph of f(x) = x² reflected over the x-axis.

Describe how the graph of g(x) = -6x² is related to the graph f(x) = x²

Reflection of f(x)=x² over the x-axis translated up 3 units

Describe how the graph of g(x) = -x²+3 is related to the graph f(x) = x²

Compression of f(x) = x² wider than the graph of f(x) = x² reflected over the x-axis translated up 5 units.

Describe how the graph of g(x) = -½x² + 5 is related to the graph f(x) = x²

Stretch of f(x)=x² narrower than the graph of f(x) = x² translated to the right 1 unit

Describe how the graph of g(x) = 4(x - 1)² is related to the graph f(x) = x²

Stretch of f(x) = x² narrower than the graph of f(x)=x²

Describe how the graph of g(x) = 7x² is related to the graph f(x) = x²

Translation of f(x)= x² up 2 units

Describe how the graph of g(x) = x² + 2 is related to the graph f(x) = x²

Translation of f(x) = x² down 8 units

Describe how the graph of g(x) = x² - 8 is related to the graph f(x) = x²

Translation of f(x) = x² to the right one unit

Describe how the graph of g(x) =(x - 1)² is related to the graph f(x) = x²

down because a = -2

Does the parabola open up or down? y=-2x²-12x+14

down because a = -1

Does the parabola open up or down? y=-x²+8x+20

up because a = 2

Does the parabola open up or down? y=2x²+20x+4

up because a = 1

Does the parabola open up or down? y=x²+4x+6

x = -3

Find the axis of symmetry for y=-2x²-12x+14

x = 4

Find the axis of symmetry for y=-x²+8x+20

x = -5

Find the axis of symmetry for y=2x²+20x+4

x=-2

Find the axis of symmetry for y=x²+4x+6

34.5

Find the mean: 39, 34, 35, 42, 45, 12,

5.5

Find the mean: 9, 7, 2, 4, 3, 5, 9, 6, 8, 0, 3, 8

44

Find the mode(s): 44, 29, 13, 44, 15

64

Find the mode(s): 89, 72, 34, 35, 35, 35, 64, 64, 77, 88, 64, 88, 64

100 and 13.5

Find the mode(s): 92, 100, 100, 23, 24, 99, 13.5, 13.5

54

Find the range: 2, 8, 10, 12, 56, 9, 5, 2, 4,

53

Find the range: 73, 45, 67, 87, 98

(0,4) maximum

Find the vertex of y = -3x ²+4. Is it a minimum or maximum point?

(1,5) maximum

Find the vertex of y=-2x²+4x+3. Is it a minimum or maximum point?

(-1.5, 10.75), maximum

Find the vertex of y=-3x²-9x+4. Is it a minimum or maximum point?

(0,-3) minimum

Find the vertex of y=x²-3. Is it a minimum or maximum point?

(2,-1) minimum

Find the vertex of y=x²-4x+3. Is it a minimum or maximum point?

(-7,0) and (1,0)

Find the x-intercepts of the function y=-2x²-12x+14.

(10,0) and (-2,0)

Find the x-intercepts of the function y=-x²+8x+20.

(-5+√23,0) and (-5-√23,0)

Find the x-intercepts of the function y=2x²+20x+4.

(0, 0) and (-10,0)

Find the x-intercepts of the function y=2x²+20x.

no x-intercepts

Find the x-intercepts of the function y=x²+4x+6.

(0, 14)

Find the y-intercept for y=-2x²-12x+14

(0, 20)

Find the y-intercept for y=-x²+8x+20

(0, 4)

Find the y-intercept for y=2x²+20x+4

(0,6)

Find the y-intercept for y=x²+4x+6

1 root

How many roots / solutions does a quadratic function have if the vertex is on the x-axis?

0 or No real solution

How many roots / solutions does a quadratic function that opens up with a vertex of (2, 4) have?

2 roots

How many roots/solutions does a quadratic function that opens down with a vertex of (2, 4) have?

No x-intercepts

How many x-intercepts does the function y=x²+3 have?

Maximum

If a quadratic function opens downward, is the vertex a maximum or a minimum?

Minimum

If a quadratic function opens upward, is the vertex a maximum or minimum?

downwards

If the a value is negative, the graph faces

upwards

If the a value is positive, the graph faces

y-axis

If the axis of symmetry is x = 0, it is also directly on the

0 solutions

If the d <0, then the quadratic equation has...

1 solution

If the d = 0, then the quadratic equation has...

2 solutions

If the d>0, then the quadratic equation has...

all real numbers

In every parabola, the domain is always

x-value

Is the axis of symmetry the x-value or y-value of the vertex?

x-int: (-3, 0) and (1, 0) y-int: (0, 3) vertex: (-1,4) axis of symmetry: x=-1

Name the coordinates of the X-INTERCEPT(S) and Y-INTERCEPT of the given function. Give the coordinates of the vertex and the axis of symmetry.

x-int: (-3, 0) and (3, 0) y-int: (0, -9) vertex: (0,-9) axis of symmetry: x=0

Name the coordinates of the X-INTERCEPT(S) and Y-INTERCEPT of the given function. Give the coordinates of the vertex and the axis of symmetry.

x-int: (0, 0) and (4, 0) y-int: (0, 0) vertex: (2,4) axis of symmetry: x=2

Name the coordinates of the X-INTERCEPT(S) and Y-INTERCEPT of the given function. Give the coordinates of the vertex and the axis of symmetry.

x-int: (1, 0) y-int: (0, 1) vertex: (1,0) axis of symmetry: x=1

Name the coordinates of the X-INTERCEPT(S) and Y-INTERCEPT of the given function. Give the coordinates of the vertex and the axis of symmetry.

x-int: NONE y-int: (0, 2) vertex: (-1,1) axis of symmetry: x=-1

Name the coordinates of the X-INTERCEPT(S) and Y-INTERCEPT of the given function. Give the coordinates of the vertex and the axis of symmetry.

range

The difference between the greatest value and the least value.

mode

The most frequently occurring number in a data set

Discriminant

The part of the quadratic formula under the square root.

Axis of Symmetry

The vertical line that passes through the vertex of the parabola is the

(2√3/3,0) and (-2√3/3,0)

What are the x-intercepts of the function y=-3x ²+4?

(-2,0)

What are the x-intercepts of the function y=x² +4x+4?

maximum; (8, 49)

What is the maximum or minimum point of y=-x² + 16x - 15?

maximum; (1, -2)

What is the maximum or minimum point of y=-x² + 2x - 3?

minimum; (-4, 32)

What is the maximum or minimum point of y=3x² + 24x + 80?

minimum; (0, 1)

What is the maximum or minimum point of y=x² + 1?

minimum; (-0.5, 2.75)

What is the maximum or minimum point of y=x² + x + 3?

minimum; (2, -8)

What is the maximum or minimum point of y=x² - 4x - 4?

10.0

What is the mean absolute deviation of these numbers? 110, 108, 100, 90, 88, 80

2.0

What is the mean absolute deviation of these numbers? 51, 57, 52, 55, 53, 50

2.9

What is the mean absolute deviation of these numbers? 90, 80, 92, 91, 88, 89

28

What is the median for this data set: 19, 27, 14, 28, 30, 51, 28 ?

20

What is the median for this data set: 20, 21, 18, 17, 20, 15, 56?

80

What is the median for this data set: 22, 83, 80, 87, 69, 66, 88 ?

Vertex

What is the point at which the parabola begins to change direction?

8

What is the value of c in y=2x²-3x+8?

(0, 2)

What is the vertex for the quadratic function f(x) = x² + 2?

(0,-25)

What is the vertex of y=x²-25?

(1.5, -12.25)

What is the vertex of y=x²-3x-10?

Down

Will the graph for the quadratic function f(x) = -2x² + 8x - 3 open up or down?

Symbol for Mean

X Bar

mean absolute deviation

one measure of variability; the average of how much the individual scores of a data set differ from the mean of the set. - abbreviation: MAD

Variance

square of standard deviation

first quartile (Q1)

the median of the lower half of a data set.

third quartile (Q3)

the median of the upper half of a data set.

median

the middle value in a data set.

mean

the sum of the data divided by the number of items in the data set.

Equation for Linear

y = x