Unit 6 January 2026 — Unit Plan

A parabola is graphed on the set of axes below.

Image Description: A coordinate plane with a parabola that opens upward with vertex at (3, -4). The parabola passes through approximately (1, 0) and (5, 0).

What are the equation of the axis of symmetry and the coordinates of the vertex of this parabola?

(1) $x = 3$ and $(3, -4)$
(2) $y = 3$ and $(3, -4)$
(3) $x = -4$ and $(-4, 3)$
(4) $y = -4$ and $(-4, 3)$

The product of $\sqrt{25}$ and $\sqrt{2}$ will result in

(1) an irrational number
(2) a rational number
(3) a natural number
(4) an integer

When $f(x) = |4x + 2|$ and $g(x) = 3x + 5$ are graphed on the same set of axes, for which value of $x$ is $f(x) = g(x)$?

(1) 1
(2) 2
(3) 3
(4) 14

The expression $x^2 - 26x - 120$ is equivalent to

(1) $(x + 4)(x - 30)$
(2) $(x - 4)(x + 30)$
(3) $(x - 20)(x + 6)$
(4) $(x + 20)(x - 6)$

The expression $3 - 2\sqrt{5} + 6\sqrt{5}$ is equivalent to

(1) $7\sqrt{5}$
(2) $7\sqrt{10}$
(3) $3 + 4\sqrt{5}$
(4) $3 + 4\sqrt{10}$

Students were asked to write a polynomial given the following conditions:

• the degree of the expression is 3
• the leading coefficient is 2
• the constant term is $-6$

Which expression satisfies all three conditions?

(1) $4x - 6 + 3x^2$
(2) $3x^2 - 6x + 4$
(3) $4 - 6x + 2x^3$
(4) $4x^2 + 2x^3 - 6$

Which graph below represents a function?

Image Description: Four graphs on coordinate planes.

Graph (1): Five points plotted at $(1, 1)$, $(2, 2)$, $(3, 2)$, $(4, 4)$, and $(5, 4)$.

Graph (3): Six points plotted at $(1, 1)$, $(2, 2)$, $(2, 3)$, $(2, 4)$, $(2, 5)$, and $(5, 4)$.

Graph (2): A step function with horizontal segments. An open circle at $(1, 1)$ with a horizontal line to a closed circle at $(3, 1)$. An open circle at $(3, 3)$ with a horizontal line to a closed circle at $(4, 3)$. A closed circle at $(4, 5)$ with a horizontal line to a closed circle at $(5, 5)$.

Graph (4): A step function with vertical segments. A closed circle at $(1, 1)$ with a vertical line to a closed circle at $(1, 3)$. A horizontal line to a closed circle at $(3, 3)$, then a vertical line up to a closed circle at $(3, 4)$. A horizontal line to an open circle at $(5, 4)$, then a vertical line up to an open circle at $(5, 5)$.

(1) Graph 1
(2) Graph 2
(3) Graph 3
(4) Graph 4

The following function models the value of a diamond ring, in dollars, $t$ years after it is purchased:

$$v(t) = 500(1.08)^t$$

What was the original price of the ring, in dollars?

(1) $108
(2) $460
(3) $500
(4) $540

The formula for the surface area of a cylinder can be expressed as $S = 2\pi r^2 + 2\pi rh$, where $r$ is the radius and $h$ is the height of the cylinder. What is the height, $h$, expressed in terms of $S$, $\pi$, and $r$?

(1) $h = \frac{S - 2\pi r^2}{2\pi r}$
(2) $h = S - r$
(3) $h = \frac{2\pi r^2 - S}{2\pi r}$
(4) $h = r - S$

When solving the following system of equations algebraically, Mason used the substitution method.

$$3x - y = 10$$

$$2x + 5y = 1$$

Which equation could he have used?

(1) $2(3x - 10) + 5x = 1$
(2) $2(-3x + 10) + 5x = 1$
(3) $2x + 5(3x - 10) = 1$
(4) $2x + 5(-3x + 10) = 1$

Which graph represents the solution to the inequality $4 + 3x > 9 - 7x$?

Image Description: Four number lines from 0 to 3 with tick marks at every $\frac{1}{2}$.

Graph (1): Open circle at $2$, arrow pointing left.

Graph (2): Open circle at $2$, arrow pointing right.

Graph (3): Open circle at $\frac{1}{2}$, arrow pointing right.

Graph (4): Open circle at $\frac{1}{2}$, arrow pointing left.

(1) Graph 1
(2) Graph 2
(3) Graph 3
(4) Graph 4

When solving the equation $3(2x + 5) - 8 = 7x + 10$, the first step could be $3(2x + 5) = 7x + 18$. Which property justifies this step?

(1) addition property of equality
(2) commutative property of addition
(3) multiplication property of equality
(4) distributive property of multiplication over addition

Which table of values best models an exponential decay function?

1. $x$	$f(x)$
   $-2$	$7$
   $-1$	$4$
   $0$	$1$
   $1$	$-2$
   $2$	$-5$
   $3$	$-8$

2. $m$	$f(m)$
   $0$	$200$
   $1$	$180$
   $2$	$162$
   $3$	$146$
   $4$	$131$
   $5$	$118$

3. $n$	$f(n)$
   $0$	$200$
   $1$	$210$
   $2$	$220$
   $3$	$231$
   $4$	$242$
   $5$	$254$

4. $p$	$f(p)$
   $-3$	$-2$
   $-2$	$-5$
   $-1$	$-5$
   $0$	$-5$
   $1$	$3$
   $2$	$3$

If $f(x) = \sqrt{x + 1} + 5$, then what is the value of $f(3)$?

(1) 9
(2) 7
(3) 3
(4) 10

Isabella wants to shift the graph of the function $f(x) = (x + 5)^2 - 2$ left 3 units. Which function represents the shifted graph?

(1) $g(x) = (x + 2)^2 - 2$
(2) $g(x) = (x + 8)^2 - 2$
(3) $g(x) = (x + 5)^2 - 5$
(4) $g(x) = (x + 5)^2 + 1$

What are the zeros of $f(x) = x(x^2 - 36)$?

(1) 0, only
(2) 6, only
(3) 6 and $-6$, only
(4) 0, 6, and $-6$

The point $(x, -6)$ lies on the graph of a parabola whose equation is $y = -x^2 - x + 6$. The value of $x$ can be

(1) $-3$ or $2$
(2) $-4$ or $3$
(3) 3, only
(4) $-4$, only

The two-way frequency table below is a summary of concession stand sales for a football game.

Of the people making a purchase at the concession stand, what is the relative frequency of them buying pizza and a water?

(1) 0.58
(2) 0.35
(3) 0.455
(4) 0.145

When Theodore was driving in Canada, his speed was 104 kilometers per hour. Theodore was asked to convert his metric speed to a different rate, using the following conversion:

$$\frac{104 \text{ km}}{1 \text{ hr}} \times \frac{1 \text{ hr}}{60 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ sec}} \times \frac{0.6214 \text{ mi}}{1 \text{ km}} \times \frac{5280 \text{ ft}}{1 \text{ mi}}$$

Assuming he did all the work correctly, what would be the units for Theodore's rate?

(1) feet per second
(2) feet per minute
(3) seconds per foot
(4) minutes per foot

Which expression is equivalent to $(-2x^2)^3$?

(1) $-2x^5$
(2) $-2x^6$
(3) $-8x^5$
(4) $-8x^6$

The table below shows the amount of a radioactive substance that remained for selected years.

To the nearest tenth, the average rate of change, in grams per year, from 2000 to 2014 is

(1) 39.1
(2) 51.8
(3) $-39.1$
(4) $-51.8$

When $2x^2 - 3x + 4$ is subtracted from $x^2 + 2x - 5$, the result is

(1) $x^2 - 5x + 9$
(2) $x^2 - x + 1$
(3) $-x^2 + 5x - 9$
(4) $-x^2 - x - 1$

Which equation has the same solution as $x^2 - 6x = 24$?

(1) $(x - 3)^2 = 24$
(2) $(x - 6)^2 = 24$
(3) $(x - 3)^2 = 33$
(4) $(x - 6)^2 = 60$

In a sequence, the first term is $-2$ and the common ratio is $-3$. The fourth term in this sequence is

(1) $-162$
(2) $-11$
(3) 24
(4) 54

Solve the equation for $x$:

$$14x = 3(1 + 2x) - 4x$$

Graph $f(x) = 3(2)^x$ over the interval $-1 \leq x \leq 2$.

Image Description: A coordinate grid is provided with the horizontal axis labeled $x$ and the vertical axis labeled $f(x)$. The grid has gridlines for plotting points.

Determine the product of $(2x + 3)$ and $(-6x^2 + 5x - 1)$.

Express the product in standard form.

A student's test scores for the semester are listed below.

83, 87, 90, 94, 94, 93, 95, 70, 72, 83, 85, 88, 98

Construct a box plot for this data set, using the number line below.

Image Description: A number line labeled "Student Test Scores" is provided, ranging from 70 to 100 with tick marks at every 2 units.

Write an equation, in slope-intercept form, of a line that passes through the point $(6, 3)$ and has a slope of $\frac{2}{3}$.

Abby has $20 to spend at a community festival. She uses $8.50 to purchase food coupons for popcorn, a hot dog, and a soda.

She can buy individual ride tickets for $2.25 each. Determine algebraically the maximum number of ride tickets Abby can buy.

A rocket was launched from the ground into the air at an initial velocity of 80 feet per second. The path of the rocket can be modeled by $h(t) = -16t^2 + 80t$, where $t$ represents the time after the rocket has been launched, and $h(t)$ represents the height of the rocket.

Image Description: A coordinate grid is provided with the horizontal axis labeled "Time (in seconds)" ranging from 0 to 6, and the vertical axis labeled "Height (in feet)" ranging from 0 to 100, with gridlines at intervals of 10 on the vertical axis and 1 on the horizontal axis.

Use the quadratic formula to solve $2x^2 - 4x - 3 = 0$, and express the answer in simplest radical form.

The table below shows the ages of drivers and the annual cost of their car insurance.

Solve the following system of inequalities graphically.

$$2y \leq x + 6$$

$$2x + y > 3$$

Label the solution set $S$.

Image Description: A coordinate grid is provided with the horizontal axis labeled $x$ and the vertical axis labeled $y$, with gridlines for plotting.

Acme Athletics purchases shoes from a supply company. In January the store bought 30 pairs of running shoes and 10 pairs of basketball shoes for $3700. In March they bought 15 pairs of running shoes and 20 pairs of basketball shoes for $3575. The supply company kept their prices constant.

If $x$ represents the cost of one pair of running shoes and $y$ represents the cost of one pair of basketball shoes, write a system of equations that models this situation.