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If , what is ?

The function $f\left(x\right)=\frac{1}{9}{\left(x-7\right)}^2+3$ gives a metal ball's height above the ground $f\left(x\right)$, in inches, $x$ seconds after it started moving on a track, where $0\le x\le 10$. Which of the following is the best interpretation of the vertex of the graph of $y=f\left(x\right)$ in the xy-plane?

The function $f\left(w\right)=6w^2$ gives the area of a rectangle, $\text{in} \text{square} \text{feet} \left({\text{ft}}^2\right)$, if its width is $w \text{ft}$ and its length is $6$ times its width. Which of the following is the best interpretation of $f\left(14\right)=\mathrm{1,176}$?

For the quadratic function $f$, the table shows three values of $x$ and their corresponding values of $f\left(x\right)$. Which equation defines $f$?

$f\left(t\right)=\mathrm{8,000}{\left(0.65\right)}^t$

The given function $f$ models the number of coupons a company sent to their customers at the end of each year, where $t$ represents the number of years since the end of $1998$, and $0\le t\le 5$. If $y=f\left(t\right)$ is graphed in the ty-plane, which of the following is the best interpretation of the y-intercept of the graph in this context?

For the function f defined above, what is the value of ?

An object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. What is the speed, in meters per second, of an object with a mass of 4 kilograms and kinetic energy of 18 joules?

In the xy-plane, a parabola has vertex $(9,-14)$ and intersects the x-axis at two points. If the equation of the parabola is written in the form $y=a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants, which of the following could be the value of $a+b+c$?

What is the y-intercept of the graph shown?

The table above gives selected values of a polynomial function p. Based on the values in the table, which of the following must be a factor of p ?

A ball is dropped from an initial height of $22$ feet and bounces off the ground repeatedly. The function $h$ estimates that the maximum height reached after each time the ball hits the ground is $85\%$ of the maximum height reached after the previous time the ball hit the ground. Which equation defines $h$, where $h\left(n\right)$ is the estimated maximum height of the ball after it has hit the ground $n$ times and $n$ is a whole number greater than $1$ and less than $10$?

What is the y-intercept of the graph shown?

The height, in feet, of an object x seconds after it is thrown straight up in the air can be modeled by the function . Based on the model, which of the following statements best interprets the equation ?

The function $f$ is defined by $f\left(x\right)=x^3+9$. What is the value of $f\left(2\right)$?

When the quadratic function $f$ is graphed in the xy-plane, where $y=f\left(x\right)$, its vertex is $\left(-3,6\right)$. One of the x-intercepts of this graph is $\left(-\frac{17}{4},0\right)$. What is the other x-intercept of the graph?

The function f is defined by . The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f ?

An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airflow , in cubic feet per minute, as a function of the angle of the fan , in degrees. According to the model, what angle, in degrees, gives the greatest airflow?

The function $f\left(t\right)=\mathrm{60,000}{\left(2\right)}^{\frac{t}{410}}$ gives the number of bacteria in a population $t$ minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

Sara opened a savings account at a bank. The table shows the exponential relationship between the time $t$, in years, since Sara opened the account and the total amount $d$, in dollars, in the account. If Sara made no additional deposits or withdrawals, which of the following equations best represents the relationship between $t$ and $d$?

A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?

$P\left(t\right)=290{\left(1.04\right)}^{\left(\frac{4}{6}\right)t}$

The function $P$ models the population, in thousands, of a certain city $t$ years after $2005$. According to the model, the population is predicted to increase by $n\%$ every $18$ months. What is the value of $n$?

For the function $f$, $f\left(0\right)=86$, and for each increase in $x$ by $1$, the value of $f\left(x\right)$ decreases by $80\%$. What is the value of $f\left(2\right)$?

The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens?

A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, , and the number of years after 2015, x ?

The function $f\left(x\right)=\mathrm{200,000}{\left(1.21\right)}^x$ gives a company’s predicted annual revenue, in dollars, $x$ years after the company started selling light bulbs online, where $0<x\le 10$. What is the best interpretation of the statement “$f\left(5\right)$ is approximately equal to $\mathrm{518,748}$” in this context?