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IM 2 Semester 1 Study Guide (12/15/2025)

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61 Nsɛmmisa

Day 2 12/11/25

Multiplying Binomial X Binomial

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Inequalities and Interval Notation

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Graphing Quadratic Functions

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Solving Quadratics

Solving Quadratic Word Problem

Simplifying Radicals

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1.

Simplify this radical.

Multiplying Radicals

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2.

Simplify this expression that contains radicals.

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3.

Simplify this expression that contains radicals.

Square Roots with Variables

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4.

Simplify each radical

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5.

Simplify each radical

Simplifying Expressions by Multiplying Exponents (Product Rule)

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6.

Simplify. Your answer should not have negative exponents.

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7.

Simplify. Your answer should not have negative exponents.

Simplifying Expressions by Dividing Exponents

(Quotient Rule)

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8.

Simplify. Your answer should not have negative exponents.

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9.

Simplify. Your answer should not have negative exponents.

Simplifying Expressions by raising Exponents by another Exponent (very meta)

(Power Rule)

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10.

Simplify. Your answer should not have negative exponents.

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11.

Simplify. Your answer should not have negative exponents.

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12.

Simplify. Your answer should not have negative exponents.

Simplifying Expressions (mixed practiced)

Using all three rules: Product Rule, Quotient Rule, and the Power Rule

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13.

Simplify. Your answer should not have negative exponents.

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14.

Simplify. Your answer should not have negative exponents.

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15.

Simplify. Your answer should not have negative exponents.

Simplifying Negative Exponents

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16.

Simplify this expression. Your answer should not have negative exponents.

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17.

Simplify this expression. Your answer should not have negative exponents.

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18.

Simplify this expression. Your answer should not have negative exponents.

Exponent Rule Recap

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19.

Use the properties of exponents to match each expression to its simplified version.

Draggable itemarrow_right_altCorresponding Item

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Identifying Parts of Expressions/Simplifying Expressions

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Monomial times a Polynomial

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27.

Find the product of these expressions. Final answers must be in standard form.

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28.

Find the product of these expressions. Final answers must be in standard form.

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29.

Find the product of these expressions. Final answers must be in standard form.

Distribute then Combine Like Terms

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30.

Distribute, then simplify the remaining expression. Final answers must be in standard form.

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31.

Write an expression in simplest form to represent the area of the shaded region.

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32.

Find the Product of this binomial * binomial using the box method.

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33.

Find the Product of this binomial * binomial using the box method.

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34.

Find the Product of this binomial * binomial using the box method.

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35.

Simplify this expression using F.O.I.L.

First-

Outside-

Inside-

Last-

Combine the four terms together for your answer

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36.

Simplify this expression using F.O.I.L.

First-

Outside-

Inside-

Last-

Combine the four terms together for your answer

Special Product: Sum and a Difference

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37.

Find the Product of these polynomials.

Special Products: Square of a Binomial

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38.

Find the square of this binomial.

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39.

Find the square of this binomial.

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40.

Use interval notation to describe the domain and range of this function.

Domain (Left to Right):

Range (Lowest to Highest):

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41.

Use interval notation to describe the domain and range of this function.

Domain (Left to Right):

Range (Lowest to Highest):

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42.

Use interval notation to describe the domain and range of this relation.

Domain (Left to Right):

Range (Lowest to Highest):

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43.

For what interval of x is the function f(x):

Increasing?

Decreasing?

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44.

For what interval of x is the function f(x):

Negative?

Positive?

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45.

What is the vertex of this parabola? Name the coordinate.

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46.

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

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47.

Describe the transformation of:

Stretch or Compression?(If a=1 or a=-1, then write none)

Opens upward or downward?

Horizontal shift? (If there is no shift write none)

Vertical shift? (If there is no shift write none)

Axis of Symmetry? (x=h)

Vertex (h,k)

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48.

Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

Left x-intercept

Right x-intercept

Axis of Symmetry

Vertex

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49.

What is the graph of this quadratic function?

Axis of Symmetry

x=

Vertex (h,k)

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50.

What is the graph of this quadratic function?

a=

b=

c=

Axis of Symmetry

x=

Vertex (h,k)

Solving Quadratic Equations by Graphing

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51.

Solve this quadratic equation graphing.

x=

x=

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52.

Solve this quadratic equation graphing.

x=

x=

Solving Quadratics by Factoring

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53.

Solve the following Quadratic function:

(7x + 3)(2x + 6) = 0

x=

x=

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54.

Solve the following Quadratic function:

x2 + 2x - 15 = 0

x=

x=

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55.

Solve the following Quadratic function:

2x2 + 5x + 2 = 0

x=

x=

Solving Quadratic Using Square Roots

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56.

Solve this quadratic equation by taking the square root

x= and

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57.

Solve this quadratic equation by taking the square root.

x= and

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Calculating Room Areas

People frequently need to calculate the area of rooms, boxes or plots of land. An example might involve building a rectangular box where one side must be twice the length of the other side.

For example, if you have only 4 square feet of wood to use for the bottom of the box, with this information, you can create an equation for the area of the box using the ratio of the two sides. This means the area -- the length times the width -- in terms of x would equal x times 2x, or 2x2. This equation must be less than or equal to four to successfully make a box using these constraints.

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60.

For this rectangle with the area given, determine the binomial factors that describe the dimensions.

Length

Width

Objects Affected by Gravity

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61.

Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t²+ 16t + 500 , where t is the time in seconds and h is the height in feet.

Round your answers to the nearest tenth.

How long did it take for Jason to reach his maximum height?

What was the highest point that Jason reached?

Jason hit the water after how many seconds?

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20.

Identify the variable terms, constant terms, and coefficients

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21.

Use page 6 in your notes to identify and classify the parts of this polynomial:

Degree (first, second, third, etc.)

# of Terms (1, 2, 3, etc.):

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22.

Use page 6 in your notes to identify and classify the parts of this polynomial:

Degree (first, second, third, etc.)

# of Terms (1, 2, 3, etc.):

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23.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

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24.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

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25.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

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26.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

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58.

Solve this quadratic equation by taking the square root.

x= and

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59.

Solve this quadratic equation by taking the square root.

x= and