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Which of the following expressions is equivalent to , for  ?

$z^2+10z-24=0$

What is one of the solutions to the given equation?

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

Which of the following is the graph in the xy-plane of the given equation?

The expression can be rewritten as , where k is a positive constant. What is the value of k ?

If , what is ?

$5x^2+10x+16=0$

How many distinct real solutions does the given equation have?

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?

If and are the two solutions to the system of equations above, what is the value of ?

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 $f\left(14\right)=\mathrm{1,176}$?

The expression is equivalent to  for some constant a. What is the value of a ?

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?

If , what is t in terms of u ?

$-9x^2+30x+c=0$

In the given equation, $c$ is a constant. The equation has exactly one solution. What is the value of $c$?

$\frac{x^2}{\sqrt{x^2-c^2}}=\frac{c^2}{\sqrt{x^2-c^2}}+39$

In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation?

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?

$8j=k+15m$

The given equation relates the distinct positive numbers $j$, $k$, and $m$. Which equation correctly expresses $j$ in terms of $k$ and $m$?

$8x+y=-11$

$2x^2=y+341$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

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?