Download Chapter 2 Review Key

Chapter 2 Review
1. Topics to study include (but are not limited to)
how to graph transformations and parabolas, to
write the quadratic equation given a graph or
information, to be able to perform operations on
imaginary numbers, find the discriminant,
calculate values of i, solve quadratic equations, and
write equations of word problems modeled with
quadratics.
2. Analyze the function
.
a.
Is its graph concave up or concave down?
b.
What is the y-intercept?
c.
What is the axis of symmetry?
d.
What is the vertex?
3. Simplify each expression. Show all of your work.
5. A basketball player stands near the middle of the
court and throws the ball toward the basket. The
path of the ball is a parabola. The ball leaves the
player’s hands at a height of 6 feet above the
ground. The ball travels to a maximum height of 12
feet when it is a horizontal distance of 18 feet from
the player. Write a function to represent the height
of the ball in terms of its distance from the player.
6. Jeremy stands on the edge of a river and throws a
rock into the water. The rock leaves his hand at a
height 5 feet above the water. It moves upward and
then down before splashing into the center of the
river. The rock reaches the highest point along its
path when it is a horizontal distance of 30 feet from
his hand and 20 feet above the water. Write a
function to represent the height of the rock in terms
of its distance from Jeremy’s hand.
7. Simplify each expression. Show all of your work.
a.
a.
b.
b.
c.
c.
4. Analyze the graph. Describe whether each function
could be used to model the graph. Explain your
reasoning.
8. Determine the number of zeros and the type of
zeros for each quadratic function. Justify your
reasoning.
a.
b.
a.
b.
Write a quadratic equation for the given
information.
9. Given two x-intercepts (
point
, 0) and (5, 0) and one
10. Given: exactly one x-intercept (2, 0) and y-intercept
11. Given: vertex
and point
Calculate each power of i.
12.
24.
13.
14.
For each complex number, write its conjugate.
15.
16.
25.
Calculate each quotient.
17.
18.
19. Graph
20. Graph
Use the Quadratic Formula to solve an equation of
the form
for each function.
without a calculator.
without a calculator.
Create a system of equations and use algebra to
write a quadratic equation for each set of three
points that lie on a parabola.
26.
27.
Use the discriminant to determine whether each
function has real or imaginary zeros.
21.
28.
Use a graphing calculator to determine the
quadratic equation for each set of three points
that lie on a parabola.
22.
23.
Write the function that represents each graph.
29.
Chapter 2 Review
Answer Section
1. ANS:
.
PTS: 1
2. ANS:
a.
concave up
b.
c.
d.
The vertex is
.
PTS: 1
REF: 2.1
NAT: A.SSE.1.a | A.SSE.2 | A.APR.1 | F.IF.4 | F.IF.9
TOP: Pre Test
KEY: standard form of a quadratic function | factored form of a quadratic function | vertex form of a quadratic
function | concavity of a parabola
3. ANS:
a.
b.
c.
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Pre Test
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
4. ANS:
a.
The function
could not model the graph because although its negative a-value means it is concave
down, it has a positive y-intercept.
b.
The function
could not model the graph because although its negative a-value means it is concave
down, both of its x-intercepts are negative.
PTS: 1
REF: 2.1
NAT: A.SSE.1.a | A.SSE.2 | A.APR.1 | F.IF.4 | F.IF.9
TOP: Mid Ch Test
KEY: standard form of a quadratic function | factored form of a quadratic function | vertex form of a quadratic
function | concavity of a parabola
5. ANS:
PTS: 1
REF: 2.1
NAT: A.SSE.1.a | A.SSE.2 | A.APR.1 | F.IF.4 | F.IF.9
TOP: End Ch Test
KEY: standard form of a quadratic function | factored form of a quadratic function | vertex form of a quadratic
function | concavity of a parabola
6. ANS:
PTS: 1
REF: 2.1
NAT: A.SSE.1.a | A.SSE.2 | A.APR.1 | F.IF.4 | F.IF.9
TOP: Mid Ch Test
KEY: standard form of a quadratic function | factored form of a quadratic function | vertex form of a quadratic
function | concavity of a parabola
7. ANS:
a.
b.
c.
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: End Ch Test
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
8. ANS:
a.
The function has 2 imaginary roots. Vertex is above the x-axis and opens up so it never intersects the
x-axis.
b.
The function has 2 real zeros that are a double root.
I know this because the function is given in vertex form with
.
PTS: 1
REF: 2.7
NAT: N.CN.7 | N.CN.8(+) | N.CN.9(+)
TOP: End Ch Test
KEY: imaginary roots | discriminant | imaginary zeros | Fundamental Theorem of Algebra | double root
9. ANS:
PTS: 1
REF: 2.5
TOP: Skills Practice
10. ANS:
NAT: A.CED.1 | F.IF.4 | F.BF.1.a
PTS: 1
REF: 2.5
TOP: Skills Practice
11. ANS:
NAT: A.CED.1 | F.IF.4 | F.BF.1.a
PTS: 1
REF: 2.5
TOP: Skills Practice
12. ANS:
NAT: A.CED.1 | F.IF.4 | F.BF.1.a
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Skills Practice
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
13. ANS:
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Skills Practice
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
14. ANS:
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Skills Practice
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
15. ANS:
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Skills Practice
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
16. ANS:
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Skills Practice
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
17. ANS:
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Skills Practice
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
18. ANS:
.
PTS: 1
REF: 2.6
NAT: N.CN.1 | N.CN.2 | N.CN.3(+) | N.CN.8(+)
TOP: Skills Practice
KEY: the imaginary number i | principal square root of a negative number | set of imaginary numbers | pure
imaginary number | set of complex numbers | real part of a complex number | imaginary part of a complex number |
complex conjugates | monomial | binomial | trinomial
19. ANS:
I start by rewriting the function as
. I plot the vertex at
to get m(x) in the form
because
of m(x) is horizontally stretched by a factor of
and
. Compared to the graph of
or 2 because
, the graph
. From the vertex, I go right 2 units and
up 1 unit to plot the point
and I go right 4 units and up 4 units to plot the point
points across the line of symmetry
and plot the corresponding points
and
points with a smooth curve to complete the graph.
PTS: 1
TOP: Assignment
20. ANS:
, where
. I reflect these last 2
. I connect the
REF: 2.4
NAT: F.IF.7.a | F.BF.3
KEY: horizontal dilation | horizontal stretching | horizontal compression
I start by rewriting the function as
. I plot the vertex at
because
of g(x) is horizontally compressed by a factor of
to get g(x) in the form
and
. Compared to the graph of
or
because
, where
the graph
. From the vertex, I go right 0.5 unit
and up 1 unit to plot the point
, I go right 1 unit and up 4 units to plot the point (5, 0), and I go right 1.5
units and up 9 units to plot the point (5.5, 5). I reflect these last 3 points across the line of symmetry
and plot
the corresponding points
, (3, 0), and (2.5, 5). I connect the points with a smooth curve to complete the
graph.
PTS: 1
TOP: Assignment
21. ANS:
Equation 1:
REF: 2.4
NAT: F.IF.7.a | F.BF.3
KEY: horizontal dilation | horizontal stretching | horizontal compression
Equation 2:
Equation 3:
Substitute equation 2 into equation 1 and solve for a.
Substitute the value for a in terms of b and the value for c into equation 3 and solve for b.
Substitute the values for b and c into equation 1 and solve for a.
Substitute the values for a, b, and c into a quadratic equation in standard form.
PTS: 1
REF: 2.5
TOP: Skills Practice
22. ANS:
NAT: A.CED.1 | F.IF.4 | F.BF.1.a
PTS: 1
REF: 2.5
TOP: Skills Practice
23. ANS:
NAT: A.CED.1 | F.IF.4 | F.BF.1.a
PTS: 1
REF: 2.5
TOP: Skills Practice
24. ANS:
NAT: A.CED.1 | F.IF.4 | F.BF.1.a
PTS: 1
REF: 2.3
NAT: F.IF.7.a | F.BF.3
TOP: Skills Practice
KEY: vertical dilation | vertical stretching | vertical compression | reflection | line of reflection
25. ANS:
PTS: 1
REF: 2.3
NAT: F.IF.7.a | F.BF.3
TOP: Skills Practice
KEY: vertical dilation | vertical stretching | vertical compression | reflection | line of reflection
26. ANS:
PTS: 1
REF: 2.7
NAT: N.CN.7 | N.CN.8(+) | N.CN.9(+)
TOP: Skills Practice
KEY: imaginary roots | discriminant | imaginary zeros | Fundamental Theorem of Algebra | double root
27. ANS:
PTS: 1
REF: 2.7
NAT: N.CN.7 | N.CN.8(+) | N.CN.9(+)
TOP: Skills Practice
KEY: imaginary roots | discriminant | imaginary zeros | Fundamental Theorem of Algebra | double root
28. ANS:
The discriminant is zero, so the function has real zeros (double roots).
PTS: 1
REF: 2.7
NAT: N.CN.7 | N.CN.8(+) | N.CN.9(+)
TOP: Skills Practice
KEY: imaginary roots | discriminant | imaginary zeros | Fundamental Theorem of Algebra | double root
29. ANS:
The discriminant is positive, so the function has real zeros.
PTS: 1
REF: 2.7
NAT: N.CN.7 | N.CN.8(+) | N.CN.9(+)
TOP: Skills Practice
KEY: imaginary roots | discriminant | imaginary zeros | Fundamental Theorem of Algebra | double root