what function can be used to model data pairs that have a common ratio
Problem ane
Which type of office all-time models each set of information points?
$(0,xi),(ane,5),(2,3),(3,5),(4,xi)$
Amrita B.
Numerade Educator
Problem 2
Which blazon of function best models each gear up of data points?
$(-4,-10),(-two,-7),(0,-4),(2,-i),(4,ii)$
Amrita B.
Numerade Educator
Problem 3
Which type of function all-time models each ready of data points?
$(-1,8),(0,4),(2,one),(3,0.5)$
Amrita B.
Numerade Educator
Problem 4
Can the $y$-values in a set of information pairs take both a mutual ratio and a common divergence? Explain why or why not.
Amrita B.
Numerade Educator
Problem 5
Explain how to decide whether a linear, exponential, or quadratic function is the about appropriate model for a ready of data.
Amrita B.
Numerade Educator
Problem half-dozen
Graph each set of points. Which model is most appropriate for each gear up?
$(-2,-three),(-ane,0),(0,ane),(1,0),(ii,-iii)$
Amrita B.
Numerade Educator
Problem vii
Graph each set of points. Which model is most advisable for each set?
$(-two,-viii),(0,-4),(3,two),(five,6)$
Amrita B.
Numerade Educator
Problem viii
Graph each prepare of points. Which model is nigh advisable for each set up?
$(-3,6),(-1,0),(0,-1),(1,-1.five)$
Amrita B.
Numerade Educator
Trouble 9
Graph each set of points. Which model is virtually advisable for each set?
$(-two,v),(-1,-one),(0,-3),(1,-1),(2,5)$
Amrita B.
Numerade Educator
Problem 10
Graph each gear up of points. Which model is most appropriate for each set up?
$\left(-1,-five \frac{2}{3}\right),(0,-v),(2,3),(3,27)$
Amrita B.
Numerade Educator
Problem 11
Graph each set of points. Which model is nearly appropriate for each set?
$(-3,eight),(-1,half dozen),(0,v),(2,3),(3,two)$
Amrita B.
Numerade Educator
Problem 12
Which type of function best models the data in each table? Use differences or ratios.
$\brainstorm{array}{|c|c|}\hline 10 & {y} \\ \hline 0 & {0} \\ \hline 1 & {1.five} \\ \hline 2 & {6} \\ \hline 3 & {13.five} \\ \hline four & {24} \\ \hline\terminate{assortment}$
Amrita B.
Numerade Educator
Problem thirteen
Which type of function all-time models the information in each table? Apply differences or ratios.
$\brainstorm{array}{|c|c|}\hline x & {y} \\ \hline 0 & {-5} \\ \hline 1 & {-3} \\ \hline two & {-1} \\ \hline 3 & {ane} \\ \hline four & {three} \\ \hline\finish{assortment}$
Amrita B.
Numerade Educator
Problem 14
$\begin{array}{|c|c|}\hline x & {y} \\ \hline 0 & {1} \\ \hline 1 & {one.2} \\ \hline 2 & {i.44} \\ \hline 3 & {ane.728} \\ \hline 4 & {ii.0736} \\ \hline\stop{array}$
Amrita B.
Numerade Educator
Problem 15
Which type of function best models the data in each table? Write an equation to model the data.
$\begin{array}{|c|c|}\hline 10 & {y} \\ \hline 0 & {0} \\ \hline 1 & {three} \\ \hline 2 & {11.3} \\ \hline 3 & {24.7} \\ \hline 4 & {43.three} \\ \hline\finish{assortment}$
Amrita B.
Numerade Educator
Problem 16
Which type of office best models the information in each table? Write an equation to model the information.
$\begin{array}{|c|c|}\hline 10 & {y} \\ \hline 0 & {5} \\ \hline 1 & {2} \\ \hline 2 & {0.79} \\ \hline 3 & {0.32} \\ \hline 4 & {0.128} \\ \hline\finish{array}$
Amrita B.
Numerade Educator
Trouble 17
Which type of part best models the data in each tabular array? Write an equation to model the data.
$\begin{array}{|c|c|}\hline x & {y} \\ \hline 0 & {2} \\ \hline 1 & {one.52} \\ \hline two & {1} \\ \hline 3 & {0.49} \\ \hline iv & {0} \\ \hline\end{assortment}$
Amrita B.
Numerade Educator
Problem 18
The number of people attending a school's first 5 football games is shown in the table below. Which type of function all-time models the data? Write an equation to model the data.
$\begin{array}{|c|c|c|c|c|}\hline \hline \text { Game } & {i} & {2} & {three} & {4} & {5} \\ \hline \text { Attendance } & {248} & {307} & {366} & {425} & {484} \\ \hline\cease{array}$
Amrita B.
Numerade Educator
Trouble xix
The average monthly balance of a savings account is shown in the table at the right. Which blazon of function best models the information? Write an equation to model the data.
Amrita B.
Numerade Educator
Trouble 20
Tom claims that, considering the data pairs $(1,four),(2,half dozen),$ $(3,9),$ and $(4,xiii.v)$ have $y$ -value with a common ratio, they are best modeled by a quadratic part. What is his error?
Amrita B.
Numerade Educator
Trouble 21
a. Brand a tabular array of five ordered pairs for each function using sequent $10$ -values. Discover the common second difference.
i. $f(x)=x^{two}-3$ $\quad$ ii. $f(x)=3 10^{ii}$ $\quad$ three. $f(x)=4 x^{2}-v x$
b. What is the relationship betwixt the common second difference and the coefficient of the $x^{2}$ -term?
c. Explain how yous could apply this human relationship to model information.
Problem 22
The number of visitors at a Web site over several days is shown in the table at the right. What is an equation that models the information?
$\cdot$ Does the graph of the data suggest a type of function to utilize?
$\cdot$ Volition your equation fit the information exactly? How exercise y'all know?
Amrita B.
Numerade Educator
Problem 23
Write a ready of data pairs that you lot could model with a quadratic part.
Amrita B.
Numerade Educator
Problem 24
A conservation organization collected the data on the number of frogs in a local wetland, shown in the table at the right. Which type of function best models the data? Write an equation to model the information.
Amrita B.
Numerade Educator
Problem 25
The table below shows the projected population of a pocket-size town. Allow $t=0$ correspond to the twelvemonth $2020 .$
a. Graph the data. Does the graph propose a linear, exponential, or quadratic model?
b. Observe the rate of change in population with respect to time from ane data pair to the side by side. How do the results support your answer to part (a)?
c. Write a part that models the data shown in the table.
d. Employ the function from role (c) to predict the town'south population in 2050 .
due east. Suppose the projected population $south$ of some other minor town is represented past the office $south=50 t+1300$. Let $t=0$ correspond to the year $2020 .$ Write an expression that can exist used to find the difference in population of the 2 towns.
$\brainstorm{assortment}{|c|c|c|c|c|}\hline \text { Yr, t } & {0} & {5} & {10} & {fifteen} \\ \hline \text { Population, p } & {5100} & {5700} & {6300} & {6900} \\ \hline\end{array}$
Problem 26
Write a quadratic function $y=a 10^{2}+b x+c$ whose graph passes through the points $(0,7),(2,13),$ and $(4,35) .$
Amrita B.
Numerade Educator
Problem 27
The diagram at the right shows the differences for the cubic function $f(10)=x^{3}-two x+v$ for the $x$ -values $0,$ $1,2,three,4,$ and $5 .$
a. Write the second and 3rd differences in the appropriate locations in the diagram.
b. What do you lot predict the 3rd departure would be if $f(6)$ were added to the diagram?
c. Do y'all think that the third differences volition be constant for other cubic functions? Explicate why or why not.
Trouble 28
The graph at the right shows the number $y$ of visitors to a museum over $10$ days. Which function models the number of visitors?
a) $y=-100 x+900$
b) $y=900(0.875)^{x}$
c) $y=-100 ten+800$
d) $y=-50 ten^{2}-400 x+1300$
Problem 29
Which expression is equivalent to $\left(4 10^{3}+ii ten^{2}+i\right)+\left(3 x^{2}+viii x+2\correct) ?$
f) $vii x^{2}+10 ten+3$
g) $seven x^{three}+10 10^{2}+3 x$
h) $4 x^{iii}+5 x^{2}+iii$
i) $four x^{3}+v 10^{2}+8 x+three$
Amrita B.
Numerade Educator
Problem 30
Which line passes through the point $(1,3)$ and is parallel to the line graphed at the correct?
a) $y=2 x+i$
b) $y=2 10+3$
c) $y=ii x-5$
d) $y=-5 10+8$
Amrita B.
Numerade Educator
Problem 31
What are the factors of $ten x^{2}-10-2 ?$ Bear witness your piece of work.
Amrita B.
Numerade Educator
Problem 32
Use the quadratic formula to solve each equation. If necessary, circular to the nearest hundredth.
$iv x^{2}+4 x-3=0$
Amrita B.
Numerade Educator
Problem 33
Use the quadratic formula to solve each equation. If necessary, round to the nearest hundredth.
$x^{2}+2 x-7=0$
Amrita B.
Numerade Educator
Trouble 34
$three x^{2}-8 x=-one$
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Numerade Educator
Trouble 35
Solve by elimination.
$x+y=x$
$x-y=2$
Amrita B.
Numerade Educator
Problem 36
Solve by elimination.
$v x-6 y=-32$
$3 x+half-dozen y=48$
Amrita B.
Numerade Educator
Trouble 37
Solve past emptying.
$-2 x+fifteen y=-32$
$7 10-five y=17$
Amrita B.
Numerade Educator
Source: https://www.numerade.com/books/chapter/quadratic-functions-and-equations/?section=7768
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