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Resources

Write a quadratic function from its x-intercepts and another point

(-10i)+(-40+8i)

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Express your answer in the form

(a+bi).

A B C

be a triangle, where the points

A, B

C

have position vectors

a, b

c

respectively. Show that the centroid of triangle

A B C

has position vector

\frac{1}{3}(a+b+c)

Simplify. Your answer should be in proper scientific notation:

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\left(2.5 \times 10^{4}\right)\left(4 \times 10^{3}\right)

Determine the intercepts of the line.

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Do not round your answers.

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\begin{array}{l} y=11 x+6 \\ x \text {-intercept: }(\square, \square) \\ y \text {-intercept: }(\square, \square) \end{array}

A circle in the

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xy

-plane has the equation

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(x-4)^{2}+(y+1)^{2}=16

. Which of the following points does NOT lie inside the circle?

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1

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(7,-3)

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(4,-1)

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(2,2)

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(0,0)

Three points on the graph of the function

f(x)

\{(0,1),(1,4),(2,9)\}

. Which equation represents

f(x)

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f(x)=5 x-1

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f(x)=4^{x}

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f(x)=(x+1)^{2}

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f(x)=3 x+1

Three points on the graph of the function

f(x)

\{(0,3),(1,9),(2,27)\}

. Which equation represents

f(x)

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f(x)=3(3)^{x}

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f(x)=18 x-9

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f(x)=x^{2}+3

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f(x)=6 x+3

Three points on the graph of the function

f(x)

\{(0,3),(1,6),(2,12)\}

. Which equation represents

f(x)

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f(x)=6 x

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f(x)=3(2)^{x}

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f(x)=3 x+3

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f(x)=x^{2}+3

Three points on the graph of the function

f(x)

\{(0,1),(1,4),(2,9)\}

. Which equation represents

f(x)

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f(x)=5 x-1

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f(x)=4^{x}

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f(x)=3 x+1

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f(x)=(x+1)^{2}

Three points on the graph of the function

f(x)

\{(0,3),(1,6),(2,9)\}

. Which equation represents

f(x)

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f(x)=3 \cdot 2^{x}

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f(x)=\frac{1}{3} x-1

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f(x)=3 x+3

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f(x)=x^{2}+3

Three points on the graph of the function

f(x)

\{(0,3),(1,6),(2,12)\}

. Which equation represents

f(x)

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f(x)=3 x+3

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f(x)=3(2)^{x}

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f(x)=x^{2}+3

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f(x)=6 x

Let the function

h

h(x)=c \cdot 2^{x-c}+k

c

k

are constants. If

h(c)=20

, which of the following equations correctly expresses

c

k ?

What is the midline equation of

y=10\cos(6x-1)-4

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an

(x, y)

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y=2 x^{2}+12 x+36

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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an

(x, y)

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y=4 x^{2}+24 x+48

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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

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y=x^{2}-12 x+43

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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

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y=4 x^{2}+32 x+52

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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

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y=-3 x^{2}-36 x-126

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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

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y=3 x^{2}-12

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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

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y=4 x^{2}-16

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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

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y=-2 x^{2}-8 x

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Find an expression which represents the sum of

(7 x-y)

(-3 x-5 y)

in simplest terms.

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Find an expression which represents the sum of

(-8 x-y)

(-7 x-5 y)

in simplest terms.

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If the equation

y=2(1.5)^{x}

is graphed in the

xy

-plane, what are the coordinates of its y-intercept?

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1

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(0,0)

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(0,1.5)

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(0,2)

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(0,3)

Which set of ordered pairs does not represent a function?

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\{(-7,-4),(-4,8),(9,-7),(-3,2)\}

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\{(-9,4),(5,-3),(3,-9),(-1,4)\}

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\{(3,-4),(1,5),(3,-1),(-6,4)\}

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\{(9,-6),(-8,-6),(-7,-1),(2,4)\}

Which set of ordered pairs represents a function?

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\{(1,9),(8,-7),(0,-7),(7,0)\}

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\{(-1,-1),(8,4),(6,1),(-1,4)\}

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\{(-4,-5),(-8,-1),(2,-3),(2,4)\}

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\{(0,-2),(-2,-8),(3,4),(-2,-6)\}

Which set of ordered pairs does not represent a function?

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\{(9,2),(-5,2),(-4,0),(1,9)\}

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\{(-3,-5),(0,8),(1,-2),(1,-9)\}

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\{(-9,-5),(-5,4),(3,4),(-6,5)\}

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\{(1,1),(-1,-8),(9,0),(6,0)\}

Which set of ordered pairs does not represent a function?

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\{(6,1),(1,-6),(5,-6),(-1,-5)\}

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\{(-5,-1),(4,-2),(-4,5),(-6,5)\}

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\{(9,8),(-5,6),(6,5),(6,0)\}

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\{(-2,4),(9,-3),(4,-3),(2,8)\}

Which set of ordered pairs does not represent a function?

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\{(-2,5),(6,-1),(-7,5),(-6,4)\}

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\{(2,-4),(-7,9),(7,8),(3,8)\}

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\{(3,-1),(3,7),(0,-3),(-4,-5)\}

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\{(8,-5),(-5,-1),(1,-5),(-7,5)\}

Which set of ordered pairs does not represent a function?

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\{(2,9),(4,-6),(4,-7),(8,4)\}

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\{(5,-1),(-8,-3),(8,6),(-7,-1)\}

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\{(5,5),(1,9),(3,9),(-7,0)\}

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\{(5,1),(0,-2),(1,1),(-1,-4)\}

Which set of ordered pairs does not represent a function?

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\{(5,-1),(2,-3),(-8,1),(-3,2)\}

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\{(1,3),(4,-9),(-7,3),(-1,6)\}

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\{(2,-4),(-3,-5),(-1,6),(-2,-5)\}

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\{(-2,-9),(3,-5),(3,1),(2,-6)\}

Which set of ordered pairs does not represent a function?

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\{(-6,7),(9,-1),(-1,-2),(-2,8)\}

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\{(-2,9),(2,5),(-4,4),(6,9)\}

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\{(8,8),(-7,-4),(9,5),(8,-6)\}

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\{(-7,-5),(8,-1),(5,0),(4,-5)\}

Which set of ordered pairs represents a function?

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\{(8,2),(-6,2),(9,3),(-6,-6)\}

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\{(4,3),(8,6),(6,3),(-8,0)\}

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\{(-6,9),(-6,8),(4,-4),(-7,-5)\}

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\{(-4,9),(3,5),(7,8),(7,-8)\}

Which set of ordered pairs does not represent a function?

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\{(-3,5),(-4,2),(-8,-1),(-6,5)\}

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\{(-8,3),(9,4),(8,1),(3,-2)\}

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\{(5,9),(3,-9),(-5,3),(3,-8)\}

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\{(9,-8),(-3,3),(-6,-3),(1,-8)\}

Which set of ordered pairs does not represent a function?

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\{(-4,-3),(-7,9),(7,-8),(-4,6)\}

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\{(-5,-4),(5,3),(-4,-7),(3,4)\}

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\{(-4,8),(0,8),(9,-3),(4,9)\}

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\{(2,-7),(-6,7),(-8,7),(-5,-5)\}

A curve is defined by the parametric equations

x(t)=3 \sin (3 t)

y(t)=-9 t^{3}-5 t^{2}+9 t

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-3 \sin (4 t)

y(t)=-2 e^{10 t}

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=9 \cos (8 t)

y(t)=-3 \cos (-t)

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=6 t^{3}+6 t+8

y(t)=-4 \cos (-2 t)

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-6 t^{3}-t-4

y(t)=7 t^{3}-5 t^{2}

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=10 \cos (9 t)

y(t)=4 e^{10 t}

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=4 t^{3}

y(t)=7 \sin (-8 t)

\frac{d y}{d x}

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If the equation

y=2(1.5)^{x}

is graphed in the

xy

-plane, what are the coordinates of its y-intercept?

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1

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(0,0)

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(0,1.5)

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(0,2)

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(0,3)

(3 g-4)(2 g-8)=a g^{2}+b g+c

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In the given equation,

a, b

c

are constants. What is the value of

a

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1

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-32

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-16

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5

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6

What is the area of the region between the graphs of

f(x)=\frac{4}{x}, g(x)=4

x=4

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1

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24-4 \ln (3)

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24-4 \ln (4)

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12-4 \ln (3)

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12-4 \ln (4)

h(x)=2^{x}

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Can we use the intermediate value theorem to say the equation

h(x)=4

has a solution where

3 \leq x \leq 5

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1

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(A) No, since the function is not continuous on that interval.

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4

h(3)

h(5)

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(C) Yes, both conditions for using the intermediate value theorem have been met.

The graph of a sinusoidal function intersects its midline at

(0,2)

and then has a minimum point at

(3,-6)

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Write the formula of the function, where

x

is entered in radians.

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f(x)=\square

The graph of a sinusoidal function has a minimum point at

(0,-10)

and then has a maximum point at

(2,-4)

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Write the formula of the function, where

x

is entered in radians.

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f(x)=\square

A=2 \pi r^{2}+2 \pi r h

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The surface area,

A

, of a cylinder of radius,

r

h

, can be found with the given equation. Which of the following correctly shows the cylinder's height in terms of its radius and surface area?

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1

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h=r-\frac{A}{2 \pi r}

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h=\frac{A}{2 \pi r}-r

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h=r-\frac{A}{r}

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h=\frac{A}{r}-r

p

p(x)=(x-a)(x-15)(x-20)

a

is a constant. Given that

p(7)=15

, what is the value of

a