Free Printable ALGEBRA RECENT MIX

1.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

2.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

3.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

4.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

5.

6^{-2 =}

a)

12

b)

-36

c)

1/36

d)

1/6

6.

Does this graph represent exponential growth or decay?

a)

Growth

b)

Decay

c)

cannot be determined

7.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

8.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

9.

What is the vertex?

a)

(5,2)

b)

(2,5)

c)

(-2,5)

d)

(-5,2)

10.

What is the axis of symmetry in the following graph?

a)

(-1,0)

b)

X=0

c)

x=-1

d)

X=1

11.

Does the following graph have a maximum or minimum.

a)

Maximum

b)

Minimum

12.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

13.

If we have the equation y=ax²+bx+c, how can we can find the x-coordinate of the vertex?

a)

-a

b)

-b/a

c)

b/2a

d)

-b/2a

14.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

15.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

both

d)

neither

16.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

17.

A parabola is upside-down when a is:

a)

negative

b)

positive

c)

0

d)

infinite

18.

Identify tha a in the quadratic equation.

f(x) = -2x² + 4x - 6

a)

-2

b)

4

c)

-6

d)

none

19.

Identify the a in the quadratic equation.

f(x) = -x²- 4x + 12.

a)

-1

b)

1

c)

4

d)

-4

e)

12

20.

Identify tha b in the quadratic equation.

f(x) = -2x² + 4x - 6

a)

-2

b)

4

c)

-6

d)

none

21.

Identify tha c in the quadratic equation.

f(x) = -2x² + 4x - 6

a)

-2

b)

4

c)

-6

d)

6

22.

What is the range of this parabola?

a)

All real #'s

b)

y > -1

c)

y < -1

d)

x > -4

23.

What is the domain of this parabola?

a)

All real #'s

b)

y > -1

c)

y < -1

d)

x > -4

24.

If h = 4, the graph will shift...

a)

up 4

b)

down 4

c)

left 4

d)

right 4

25.

If k = 3, the graph will shift ...

a)

up 3

b)

down 3

c)

left 3

d)

right 3

26.

Given the function $y=\left(x+4\right)^2+2$ , what is the parent function?

a)

$y=x^2$

b)

$y=a\left(x-h\right)^2+k$

c)

$y=mx+b$

d)

$y=0\left(x-0\right)^2+0$

27.

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

a)

$y=-\left|x-15\right|-3$

b)

$y=-\left|x+15\right|-3$

c)

$y=\frac{1}{2}\left|x+3\right|-15$

d)

$y=\frac{1}{2}\left|x-3\right|-15$

e)

$y=\left|-x-15\right|-3$

28.

Which transformations are involved in the equation $y=\frac{1}{2}\sqrt{x+1}-1$ ?

a)

Horizontal translation left

b)

Vertical shrink

c)

Vertical translation down

d)

Horizontal translation right

e)

Vertical stretch

29.

If $f\left(x\right)=a\left(x-h\right)^2+k$ has a horiz. shift of -2, a vertical shift of +3 and a vertical stretch of 4, what are the values of a, h, and k?

a)

$a=4;\ h=-2;\ k=3$

b)

$a=2;\ h=4;\ k=-3$

c)

$a=4;\ h=2;\ k=3$

d)

$a=3;\ h=2;\ k=-4$

30.

Which of the following are contained in the pictured graph

a)

A minimum

b)

a maximum

c)

a quadratic function

d)

an absolute value function

e)

a y-intercept at 0.

31.

What is the vertex form of a quadratic function?

a)

f(x) = 2a(x-h)² + k

b)

f(x) = a(x-h)² + k

c)

f(x) = (x+h)² + k

d)

f(x) = a(x-h) - k

32.

What is the axis of symmetry in a function?

a)

The transformation of the graph

b)

The vertex, represented by (h,k)

c)

A vertical line that passes through the vertex and divides the parabola in half

d)

y = h

33.

Identify the minimum and the domain of the function y = -2(x+1)² + 4

a)

Max: 4, Domain: All Real Numbers

b)

Min: -4, Domain: All Real Numbers

c)

Max: 2, Domain: All real numbers when x is greater than 4

d)

Min: -2, Domain: All real numbers when x is less than 4

34.

Does the function y = (x+2)² have a maximum or minimum?

a)

Maximum

b)

Minimum

c)

Both

d)

Neither

35.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

36.

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

a)

Compressed by 1/2, shifted 4 units right and 1 unit up

b)

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

c)

Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

d)

Stretched by 1/2, shifted 4 units right and 1 unit down

37.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

38.

What steps transform the graph y = x² to y = (x-4)²

a)

Shifted down 4 units

b)

Shifted left 4 units

c)

Shifted right 4 units

d)

Shifted up 4 units

39.

to change any number into a value of one

a)

give it a negative sign

b)

give it an exponent of zero

c)

give it an exponent of one

d)

multiply it by -1

40.

which is the base of $6^5$

a)

6

b)

5

c)

7776

41.

a negative exponent sign will always result in a

a)

negative number

b)

fraction

c)

negative fraction

d)

zero

ALGEBRA RECENT MIX

Total questions: 41

Worksheet time: 48mins

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