Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Chapter 3 Test Review
Students Will Be Able To:
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Use the quadratic formula to solve (find the roots of) a quadratic equation (TB 3.02)
Use the discriminant (𝑏 ! − 4𝑎𝑐) to determine how many real solutions a quadratic
equation has and whether the real solutions are rational or irrational (TB 3.02)
Find (multiple) quadratic equations that have a given pair of roots (solutions) (TB 3.03)
Use factoring (including GCF, Difference of squares, monic quadratic factoring and
non-monic quadratic factoring) to find solutions to polynomials (TB 3.04)
Graph quadratic functions efficiently from vertex form, standard/normal form, and
factored form of a quadratic equation (TB 3.07 and TB 3.08)
Graph quadratic functions when given some of the critical values (TB 3.07 and TB 3.08)
Model projectile motion with quadratic function and find values such as launch point,
vertex, landing point within the context of the problem (TB 3.07)
Convert between different forms of a quadratic equation (TB 3.08)
Vocabulary: Find and write definitions for each of the vocabulary words below. You should
know all of these words and be able to use them in context.
Factor an Expression
Coefficient
Linear Polynomial
Polynomial
Quintic Polynomial
Trinomial
Quadratic Equation
Vertex Form
Solve a Quadratic
Equation
Expand an Expression
Cubic Polynomial
Linear Term
Quadratic Polynomial
Difference of Squares
Perfect Square Trinomial
Line of Symmetry
Maximum of a Parabola
y-Intercept
Greatest Common Factor
Cubic Term
Monomial
Quadratic Term
Completing the Square
Monic Equation
Parabola
Minimum of a Parabola
Factored Form of a
quadratic (aka Intercept
form)
Identity
Degree of a Polynomial
Standard (Normal) Form
Quartic Polynomial
Binomial
Non-Monic Equation
Vertex
Roots, Zeros, x-intercepts
Practice Problems: All of this can be done without a graphing calculator. A scientific (NONGRAPHING) calculator is acceptable and will be allowed on the test.
1. Describe how to find the vertex of a parabola from each of the following forms of the
equation.
a. Vertex form
b. Standard form
c. Factored form
2. A parabola has a vertex at (3, -8) and passes through the point (5, 20). Write an
equation of the parabola in vertex form.
3. A parabola has zeros at 4 and -3. Write an equation in intercept form (factored form) so
that the y-intercept is (0, 6).
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
2
4. Here is a quadratic in vertex form: y = 4(x − 2) −100
Calculate your points and think about your scaling before graphing anything. If you need to
graph as you go, use scrap paper!
€
Sketch a graph clearly labeling:
The vertex
The zeros
The axis of symmetry
The y-intercept
A mirror/sister point
5. Here is a quadratic in intercept form: y = −4(x − 2.5)(x + 8.5) .
Calculate your points and think about your scaling before graphing anything. If you need to
“graph as you go,” use scrap paper!
Free Multi-Width
Graph Paper from http://incompetech.com/graphpaper/
€
Sketch a graph clearly labeling:
The vertex
The zeros
The axis of symmetry
The y-intercept
A mirror/sister point
Free Multi-Width Graph Paper from http://incompetech.com/graphpaper/m
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
6. Solve by any method you choose.
a. 3x 2 − 48 = 0
b.
c. x 6 − 9x 4 = 0
d. x 3 = 16x
x 2 + 4 x = −4
€
e. 8x2 + 14x – 15 = 0
f. 3(2x + 1)2 = (2x + 1)
€
€
g.
5x2
h. 3(x + 5) 2 = 0
– 20x = 62
x2
14x
+3=
4
€ 2
i. x2 +1.5x + 3.5 = 0
j.
7. Given equation 2x 2 − 20x +15 = 0
a. Solve by completing the square:
b. solve using the quadratic formula
8. Put in€vertex form:
a. y = 5x 2 +12x − 8
b. y = 3x 2 +18x −11
€
9. A ball is thrown upward from a flat surface. Its height in feet as a function of time since it
€ was thrown (in seconds) is given by the equation y = −5t 2 + 34t + 25 .
a. What was the highest the ball got, and when did it reach that height?
b. When does the ball land?
€
c. What does the 25 in the equation signify?
d. Graph the situation using an appropriate
domain.
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Extra Practice: If you can do all the problems above correctly, you are in good shape. Here are
some extra practice problems if you need more work on a particular topic.
I.
Factoring Non-Monic Quadratics (TB 3.04)
1. Factor:
2. Factor:
3. Factor:
II.
Solving Quadratic Equations (TB 2.10, 2.11, 3.02)
III.
Finding the Equation of a Quadratic Function (TB 3.03)
4.
5.
6.
7.
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
IV.
Graphing Quadratic Functions (TB 3.07, 3.08)
V.
Modeling Projectile Motion
Name:
Date:
8.
9.
10.
11.
12.
13. A ball is thrown from some unknown height. After 3 seconds, its height is 50 meters and
after 5 seconds its height is 10 meters.
a. Write the function h(t ) = −5t 2 + bt + c . Use the two points given to find b and c.
b. Exactly when does the ball land?
c. What is the highest the ball got and when did it reach that height?
14. A small rocket is launched from the top of a building. Its height (in meters) as a function of
time (in seconds) is given by the equation h(t ) = −5t 2 + 40t + 100 .
a. How high is it after 3 seconds?
b. How tall is the building?
c. What two times is its height 100 meters?
d. When is its height 160 meters?
e. When does it land?
f. What is its maximum height and when is it attained?