Resources

Resources

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

f

is a quadratic function. The graph of

y = f(x)

xy

-plane has a vertex at

(6, 10)

, contains the point

(5, 8)

y

(0, a)

y = 4f(x)

y

(0, b)

. What is the positive difference between

a

b

How many sides does a heptagon have?

\newline

\newline

5

\newline

4

\newline

7

\newline

10

How many sides does a quadrilateral have?

\newline

\newline

3

\newline

8

\newline

4

\newline

7

Select the expressions that are equivalent to

7(n + 1)

\newline

Multi-select Choices:

\newline

7n + 7

\newline

8n

\newline

1(7 + n)

\newline

(1 + n)7

Identify the center and radius.

\newline

x^{2}+(y+2)^{2}=64

Identify the center and radius.

\newline

(x-2)^{2}+(y+3)^{2}=36

Write the equation of the parabola that passes through the points

(-5,-36)

(-3,0)

(-2,0)

. Write your answer in the form

y=a(x–p)(x–q)

a

p

q

are integers, decimals, or simplified fractions.

What is the value of the expression

2x^{3}y

x=-2

y=3

\newline

1

-192

\newline

2

-108

\newline

3

-48

\newline

4

48

Write a quadratic equation for a parabola that passes through the points

(-1,-3)

(0,-4)

(2,6)

using quadratic regression.

Which of the following points

(x, y)

lies on the graph of

8 x+2 y=24 ?

\newline

(-1,8)

\newline

(2,8)

\newline

(6,-12)

\newline

(8,2)

Function A is a linear function whose graph includes the points

(-8,-21)

(8,-7)

\newline

Which of the following functions has the same slope as Function A?

\newline

\newline

y = \frac{7}{8}x + 14

\newline

y = -14x + \frac{7}{8}

\newline

y = 14x - \frac{7}{8}

\newline

y = -\frac{7}{8}x - 14

Function A is a linear function whose graph includes the points

(0,-7)

(3,0)

\newline

Which of the following functions has the same

y

-intercept as Function A?

\newline

\newline

y = -7

\newline

y = \frac{7}{3}x

\newline

y = -\frac{7}{3}x

\newline

y = 3

18p-36

to identify the equivalent expressions.

\newline

2

\newline

3(9p-12)

\newline

9(2p-4p)

\newline

2(9p-18)

\newline

18(p-2)

99-45 f+36 b

to identify the equivalent expressions.

\newline

2

\newline

9(11-5f+4b)

\newline

3(33-15+12)

\newline

11(9-4f+3b)

\newline

3(33-15 f+12 b)

p

x=-2, x=\frac{1}{3}

x=3

\newline

What could be the equation of

p

\newline

1

\newline

p(x)=(x+2)(x+3)(3 x+1)

\newline

p(x)=(x+2)(x+3)(3 x-1)

\newline

p(x)=(x+2)(x-3)(3 x-1)

\newline

p(x)=(x-2)(x+3)(3 x+1)

p

x=0, x=-\frac{1}{6}

x=-3

\newline

What could be the equation of

p

\newline

1

\newline

p(x)=x(6 x+1)(x+3)

\newline

p(x)=x(6 x-1)(x-3)

\newline

p(x)=x\left(\frac{1}{6} x\right)(x+3)

\newline

p(x)=x\left(-\frac{1}{6} x\right)(x-3)

p

x=5, x=-1

x=-\frac{1}{4}

\newline

What could be the equation of

p

\newline

1

\newline

p(x)=(x+5)(x+1)(4 x+1)

\newline

p(x)=(x-5)(x+1)(4 x+1)

\newline

p(x)=(x+5)(x-1)(4 x-1)

\newline

p(x)=(5 x)(-1 x)\left(-\frac{1}{4} x\right)

C

\newline

y=2+10x^{\frac{1}{2}}-2x^{\frac{3}{2}},\quad x > 0

\newline

(a)

\frac{dy}{dx}

giving your answer in simplest form.

x y

-plane, the graph of a rational function

f

has a vertical asymptote at

x=-5

. Which of the following could be an expression for

f(x)

\newline

\frac{(x-5)(x+5)}{2(x-5)}

\newline

\frac{(x-4)(x+5)}{(x-1)(x+5)}

\newline

\frac{(x+1)(x+5)}{(x-5)(x+2)}

\newline

\frac{(x-5)(x-3)}{(x-3)(x+5)}

Given the set of zeros

\{-5,1, \pm 2 i\}

, which is a polynomial of least degree in factored form with a leading coefficient of one?

\newline

f(x)=(x-5)(x+1)\left(x^{2}-4\right)

\newline

f(x)=(x+5)(x-1)\left(x^{2}+2\right)

\newline

f(x)=(x-5)(x+1)(x+2 i)^{2}

\newline

f(x)=(x+5)(x-1)\left(x^{2}+4\right)

Write the equation of the parabola that passes through the points

(1,0)

(6,0)

(7,30)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-4,18)

(-3,0)

(-1,0)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(1,0)

(3,0)

(5,40)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-9,-16

(-5,0

(-4,0

\newline

Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-3,0

(-2,-12

(1,0

\newline

Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-3,0

(-2,-60

(4,0

\newline

Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(3,0)

(2,-27)

(-1,0)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-3,-14

(-5,0

(2,0

). Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-6,-15)

(-1,0)

(-7,0)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Show that the points

A(1,3), B(4,3), C(4,6)

D(1,6)

are the vertices of a square.

The solution of an equation

u_{y y}+16 u=0

\newline

c_{1}(y) \cos 4 y+c_{2}(y) \sin 4 y

\newline

c_{1}(x) \cos 4 y+c_{2}(x) \sin 4 y

\newline

c_{1}(x) \cos 4 x+c_{2}(x) \sin 4 x

\newline

c_{1}(x) \cos 4 y+c_{2}(x) \sin 4 x

Give the equation of a circle with a diameter that has endpoints

(10,-8)

(-6,0)

Find the coordinates of the vertex of

y=3(x-1)^{2}+4

Simplify the expression to a + bi form:

\newline

(-11+4 i)(10+7 i)

\newline

Simplify the expression to a + bi form:

\newline

(-9+i)(-11+5 i)

\newline

Express as a complex number in simplest a+bi form:

\newline

\frac{12-21 i}{-6-9 i}

\newline

Express as a complex number in simplest a+bi form:

\newline

\frac{9+21 i}{2-5 i}

\newline

Express as a complex number in simplest a+bi form:

\newline

\frac{-2+5 i}{-1+i}

\newline

Express as a complex number in simplest a+bi form:

\newline

\frac{24+23 i}{-9+2 i}

\newline

Express as a complex number in simplest a+bi form:

\newline

\frac{-7+9 i}{-5-i}

\newline

Express as a complex number in simplest a+bi form:

\newline

\frac{-5-20 i}{-6-7 i}

\newline

Express as a complex number in simplest a+bi form:

\newline

\frac{-2+9 i}{-3-i}

\newline

Solve the equation below for

x

a

\newline

4(a x + 3) - 3 a x = 25 + 3 a

x

-intercepts of the following equation.

\newline

(x+5)(x-4)=y

\newline

(0,-5)

(0,4)

\newline

(0,-20)

\newline

(-5,0)

(-4,0)

\newline

(-5,0)

(4,0)

\newline

(0,20)

\newline

(-20,0)

x

-intercepts of the following equation.

\newline

(-x-4)(x+3)=y

\newline

(0,-4)

(0,-3)

\newline

(-4,0)

(-3,0)

\newline

(0,-12)

\newline

(0,12)

\newline

(-4,0)

(3,0)

\newline

(-12,0)

y

-intercept of the following equation.

\newline

(x-5)(x+4)=y

\newline

(5,0)

(-4,0)

\newline

(-20,0)

\newline

(0,5)

(0,-4)

\newline

(0,-20)

\newline

(-5,0)

(-4,0)

\newline

(0,20)

y

-intercept of the following equation.

\newline

(-x+4)(x+3)=y

\newline

(0,12)

\newline

(0,4)

(0,-3)

\newline

(0,-12)

\newline

(12,0)

\newline

(4,0)

(-3,0)

\newline

(-4,0)

(-3,0)

x

-intercepts of the following equation.

\newline

(-x-1)(x-3)=y

\newline

(3,0)

\newline

(-1,0)

(3,0)

\newline

(0,3)

\newline

(0,-3)

\newline

(0,-1)

(0,3)

\newline

(-1,0)

(-3,0)

y

-intercept of the following equation.

\newline

(-x-2)(-x-3)=y

\newline

(2,0)

(-3,0)

\newline

(-2,0)

(-3,0)

\newline

(0,-6)

\newline

(0,6)

\newline

(6,0)

\newline

(0,-2)

(0,-3)

x

-intercepts of the following equation.

\newline

(x+1)(x-3)=y

\newline

(0,-1)

(0,3)

\newline

(-3,0)

\newline

(0,3)

\newline

(0,-3)

\newline

(-1,0)

(3,0)

\newline

(-1,0)

(-3,0)