Complete each of the following to form a true statement.

The principle of square roots states that if $x^{2}=k$ then $x=-$_____ or $x=$_____

Melissa S.

Numerade Educator

Complete each of the following to form a true statement.

If $(x+5)^{2}=49,$ then $x+5=$_____ or $x+5=$_____

Melissa S.

Numerade Educator

Complete each of the following to form a true statement.

If $t^{2}+6 t+9=17,$ then (_____)$^{2}=17$ and

_____$=\pm \sqrt{17}$

Melissa S.

Numerade Educator

Complete each of the following to form a true statement.

The equations $x^{2}+8 x+$ _____ $=23$ and $x^{2}+8 x=7$ are equivalent.

Melissa S.

Numerade Educator

Complete each of the following to form a true statement.

The expressions $t^{2}+10 t+$_____ and $(t+$_____$)^{2}$ are equivalent.

Melissa S.

Numerade Educator

Complete each of the following to form a true statement.

The expressions $x^{2}-6 x+$_____ and $(x-$_____$)^{2}$ are equivalent.

Melissa S.

Numerade Educator

Determine the number of real-number solutions of each equation from the given graph.

$$

\begin{array}{c}

{x^{2}+x-12=0} \\

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

\end{array}

$$

(GRAPH CANNOT COPY)

Melissa S.

Numerade Educator

Determine the number of real-number solutions of each equation from the given graph.

$$

\begin{array}{c}

{-3 x^{2}-x-7=0} \\

{y=-3 x^{2}-x-7}

\end{array}

$$

(GRAPH CANNOT COPY)

Melissa S.

Numerade Educator

Determine the number of real-number solutions of each equation from the given graph.

$$

\begin{aligned}

4 x^{2}+9 =12 x \\

y =12 x-4 x^{2}-9

\end{aligned}

$$

(GRAPH CANNOT COPY)

Melissa S.

Numerade Educator

Determine the number of real-number solutions of each equation from the given graph.

$$

\begin{aligned}

2 x^{2}+3 =6 x \\

y =2 x^{2}+3-6 x

\end{aligned}

$$

(GRAPH CANNOT COPY)

Melissa S.

Numerade Educator

Determine the number of real-number solutions of each equation from the given graph.

$$

\begin{aligned}

&f(x)=0\\

&y=f(x)

\end{aligned}

$$

(GRAPH CANNOT COPY)

Melissa S.

Numerade Educator

$$

\begin{aligned}

&f(x)=0\\

&y=f(x)

\end{aligned}

$$

(GRAPH CANNOT COPY)

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$x^{2}+16 x+$_____$=(x+$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$x^{2}+8 x+$_____$=(x+$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$t^{2}-10 t+$_____$=(t-$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$t^{2}-6 t+$_____$=(t-$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$t^{2}-2 t+$_____$=(t-$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$x^{2}+2 x+$_____$=(x+$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$x^{2}+3 x+$_____$=(x+$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$t^{2}-9 t+$_____$=(t-$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$x^{2}+\frac{2}{5} x+$_____$=(x+$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$x^{2}+\frac{2}{3} x+$_____$=(x+$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$t^{2}-\frac{5}{6} t+$_____$=(t-$_____$)^{2}$

Melissa S.

Numerade Educator

Replace the blanks in each equation with constants to complete the square and form a true equation.

$t^{2}-\frac{5}{3} t+$_____$=(t-$_____$)^{2}$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

x^{2}+6 x=7

$$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

x^{2}+8 x=9

$$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

t^{2}-10 t=-23

$$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

t^{2}-4 t=-1

$$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

x^{2}+12 x+32=0

$$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

x^{2}+16 x+15=0

$$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

t^{2}+8 t-3=0

$$

Melissa S.

Numerade Educator

Solve by completing the square. Show your work.

$$

t^{2}+6 t-5=0

$$

Melissa S.

Numerade Educator

Complete the square to find the $x$ -intercepts of each function given by the equation listed.

$$

f(x)=x^{2}+6 x+7

$$

Melissa S.

Numerade Educator

Complete the square to find the $x$ -intercepts of each function given by the equation listed.

$$

f(x)=x^{2}+10 x-2

$$

Melissa S.

Numerade Educator

Complete the square to find the $x$ -intercepts of each function given by the equation listed.

$$

g(x)=x^{2}+9 x-25

$$

Melissa S.

Numerade Educator

Complete the square to find the $x$ -intercepts of each function given by the equation listed.

$$

g(x)=x^{2}+5 x+2

$$

Melissa S.

Numerade Educator

Complete the square to find the $x$ -intercepts of each function given by the equation listed.

$$

f(x)=x^{2}-10 x-22

$$

Melissa S.

Numerade Educator

Complete the square to find the $x$ -intercepts of each function given by the equation listed.

$$

f(x)=x^{2}-8 x-10

$$

Melissa S.

Numerade Educator

Solve by completing the square. Remember to first divide, as in Example $11,$ to make sure that the coefficient of $x^{2}$ is 1.

$$

9 x^{2}+18 x=-8

$$

Melissa S.

Numerade Educator

Solve by completing the square. Remember to first divide, as in Example $11,$ to make sure that the coefficient of $x^{2}$ is 1.

$$

4 x^{2}+8 x=-3

$$

Melissa S.

Numerade Educator

Solve by completing the square. Remember to first divide, as in Example $11,$ to make sure that the coefficient of $x^{2}$ is 1.

$$

3 x^{2}-5 x-2=0

$$

Melissa S.

Numerade Educator

Solve by completing the square. Remember to first divide, as in Example $11,$ to make sure that the coefficient of $x^{2}$ is 1.

$$

2 x^{2}-5 x-3=0

$$

Melissa S.

Numerade Educator

Solve by completing the square. Remember to first divide, as in Example $11,$ to make sure that the coefficient of $x^{2}$ is 1.

$$

5 x^{2}+4 x-3=0

$$

Melissa S.

Numerade Educator

Solve by completing the square. Remember to first divide, as in Example $11,$ to make sure that the coefficient of $x^{2}$ is 1.

$$

4 x^{2}+3 x-5=0

$$

Melissa S.

Numerade Educator

Find the $x$ -intercepts of the function given by $f(x)=4 x^{2}+2 x-3$.

Melissa S.

Numerade Educator

Find the $x$ -intercepts of the function given by $f(x)=3 x^{2}+x-5$.

Melissa S.

Numerade Educator

Find the $x$ -intercepts of the function given by $g(x)=2 x^{2}-3 x-1$.

Melissa S.

Numerade Educator

Find the $x$ -intercepts of the function given by $g(x)=3 x^{2}-5 x-1$.

Melissa S.

Numerade Educator

Use $A=P(1+r)^{t}$ to find the interest rate. Refer to Example $12 .$

2000 dollars grows to 2420 dollars in 2 years

Melissa S.

Numerade Educator

Use $A=P(1+r)^{t}$ to find the interest rate. Refer to Example $12 .$

1000 dollars grows to 1440 dollars in 2 years

Melissa S.

Numerade Educator

Use $A=P(1+r)^{t}$ to find the interest rate. Refer to Example $12 .$

6250 dollars grows to 6760 dollars in 2 years

Melissa S.

Numerade Educator

Use $A=P(1+r)^{t}$ to find the interest rate. Refer to Example $12 .$

6250 dollars grows to 7290 dollars in 2 years

Melissa S.

Numerade Educator

Use $s=16 t^{2}$. Refer to Example 13 and neglect air resistance.

The Grand Canyon skywalk is 4000 ft above the Colorado River. How long will it take a stone to fall from the skywalk to the river? Source: www.grandcanyonskywalk.com (IMAGE CANNOT COPY)

Melissa S.

Numerade Educator

Use $s=16 t^{2}$. Refer to Example 13 and neglect air resistance.

The Sears Tower in Chicago is 1454 ft tall. How long would it take an object to fall freely from the top?

Melissa S.

Numerade Educator

Use $s=16 t^{2}$. Refer to Example 13 and neglect air resistance.

At $2063 \mathrm{ft}$, the KVLY-TV tower in North Dakota is the tallest supported tower in the United States. How long would it take an object to fall freely from the top? Source: North Dakota Tourism Division.

Melissa S.

Numerade Educator

Use $s=16 t^{2}$. Refer to Example 13 and neglect air resistance.

El Capitan in Yosemite National Park is 3593 ft high. How long would it take a carabiner to fall freely from the top? Source: Guinness World Records 2008 (IMAGE CANNOT COPY)

Melissa S.

Numerade Educator

Explain in your own words a sequence of steps that can be used to solve any quadratic equation in the quickest way.

Melissa S.

Numerade Educator

Describe how to write a quadratic equation that can be solved algebraically but not graphically.

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Evaluate. [ 1.8]

$$

b^{2}-4 a c, \text { for } a=3, b=2, \text { and } c=-5

$$

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Evaluate. [ 1.8]

$$

b^{2}-4 a c, \text { for } a=1, b=-1, \text { and } c=4

$$

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Simplify. $[10.3],[10.8]$

$$

\sqrt{200}

$$

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Simplify. $[10.3],[10.8]$

$$

\sqrt{96}

$$

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Simplify. $[10.3],[10.8]$

$$

\sqrt{-4}

$$

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Simplify. $[10.3],[10.8]$

$$

\sqrt{-25}

$$

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Simplify. $[10.3],[10.8]$

$$

\sqrt{-8}

$$

Melissa S.

Numerade Educator

To prepare for Section $11.2,$ review evaluating expressions and simplifying radical expressions (Sections $1.8,10.3$ and $10.8)$ Simplify. $[10.3],[10.8]$

$$

\sqrt{-24}

$$

Melissa S.

Numerade Educator

What would be better: to receive $3 \%$ interest every 6 months or to receive $6 \%$ interest every 12 months? Why?

Melissa S.

Numerade Educator

Example 12 was solved with a graphing calculator by graphing each side of

$$

4410=4000(1+r)^{2}

$$

How could you determine, from a reading of the problem, a suitable viewing window?

Melissa S.

Numerade Educator

Find $b$ such that each trinomial is a square.

$$

x^{2}+b x+81

$$

Melissa S.

Numerade Educator

Find $b$ such that each trinomial is a square.

$$

x^{2}+b x+49

$$

Melissa S.

Numerade Educator

If $f(x)=2 x^{5}-9 x^{4}-66 x^{3}+45 x^{2}+280 x$ and $x^{2}-5$ is a factor of $f(x),$ find all $a$ for which $f(a)=0$.

Melissa S.

Numerade Educator

If $f(x)=\left(x-\frac{1}{3}\right)\left(x^{2}+6\right)$ and $g(x)=$ $\left(x-\frac{1}{3}\right)\left(x^{2}-\frac{2}{3}\right),$ find all $a$ for which $(f+g)(a)=0$.

Melissa S.

Numerade Educator

A barge and a fishing boat leave a dock at the same time, traveling at a right angle to each other. The barge travels $7 \mathrm{km} / \mathrm{h}$ slower than the fishing boat. After 4 hr, the boats are $68 \mathrm{km}$ apart. Find the speed of each boat. (IMAGE CANNOT COPY)

Melissa S.

Numerade Educator

Find three consecutive integers such that the square of the first plus the product of the other two is 67 .

Melissa S.

Numerade Educator