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In the xy-plane, a line with equation $2y=c$ for some constant $c$ intersects a parabola at exactly one point. If the parabola has equation $y=-2x^2+9x$, what is the value of $c$?

Which of the following could be the equation of the graph shown in the xy-plane?

$f\left(x\right)=4x^2+64x+262$

The function $g$ is defined by $g\left(x\right)=f\left(x+5\right)$. For what value of $x$ does $g\left(x\right)$ reach its minimum?

The graph of $y=f\left(x\right)$ is shown, where the function $f$ is defined by $f\left(x\right)=a{x}^3+b{x}^2+cx+d$ and $a$, $b$, $c$, and $d$ are constants. For how many values of $x$ does $f\left(x\right)=0$?

Which expression is equivalent to $11x^3-5x^3$?

Which expression is equivalent to $50x^2+5x^2$?

The table shown includes some values of x and their corresponding values of y. Which of the following graphs in the xy-plane could represent the relationship between x and y ?

The expression $\left(3x-23\right)\left(19x+6\right)$ is equivalent to the expression $a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

Which expression is equivalent to $20w-\left(4w+3w\right)$?

Which expression is equivalent to $\frac{4}{4x-5}-\frac{1}{x+1}$?

The function $f$ is defined by $f\left(x\right)=\left(x-6\right)\left(x-2\right)\left(x+6\right)$. In the xy-plane, the graph of $y=g\left(x\right)$ is the result of translating the graph of $y=f\left(x\right)$ up $4$ units. What is the value of $g\left(0\right)$?

Which of the following is equivalent to ?

The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution $\left(x,y\right)$ to this system?

What is the product of the solutions to the given equation?

In the expression above, b and c are positive integers. If the expression is equivalent to and , which of the following could be the value of c ?

What is the solution to the equation above?

A rectangle has a length of $x$ units and a width of $\left(x-15\right)$ units. If the rectangle has an area of $76$ square units, what is the value of $x$?

A scientist initially measures $\mathrm{12,000}$ bacteria in a growth medium. $4$ hours later, the scientist measures $\mathrm{24,000}$ bacteria. Assuming exponential growth, the formula $P=C{\left(2\right)}^{rt}$ gives the number of bacteria in the growth medium, where $r$ and $C$ are constants and $P$ is the number of bacteria $t$ hours after the initial measurement. What is the value of $r$?

$\sqrt{{\left(x-2\right)}^2}=\sqrt{3x+34}$

What is the smallest solution to the given equation?

If the ordered pair satisfies the system of equations above, what is one possible value of x ?

A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The model estimates that the projectile was launched from an initial height of $7$ meters above the ground and reached a maximum height of $51.1$ meters above the ground $3$ seconds after the launch. How many seconds after the launch does the model estimate that the projectile will return to a height of $7$ meters?

$y=x^2-14x+22$

The given equation relates the variables $x$ and $y$. For what value of $x$ does the value of $y$ reach its minimum?

Which of the following expressions is equivalent to the expression above?

Which expression is equivalent to $\left(d-6\right)\left(8d^2-3\right)$?

An oceanographer uses the equation to model the speed s, in knots, of an ocean wave, where p represents the period of the wave, in seconds. Which of the following represents the period of the wave in terms of the speed of the wave?