Topic Question Set
Q 1
:
A highway underpass has a parabolic shape. A parabola is the graph that results from p(x) = ax² + bx + c. Parabolas are symmetric about a vertical line known as the Axis of Symmetry.
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
Based on the given information, answer the following questions:
(i) If the highway overpass is represented by x² - 2x - 8, then find its zeros.
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
4 and -2.
4 and 3.
-4 and -2.
3 and -2.
(1)
Given polynomial is x² - 2x - 8.
⇒ x² - 4x + 2x - 8 (By mid-term splitting)
⇒ x(x - 4) + 2(x - 4)
⇒ (x - 4)(x + 2)
So, the zeros are 4 and -2.
Q 2
:
A highway underpass has a parabolic shape. A parabola is the graph that results from p(x) = ax² + bx + c. Parabolas are symmetric about a vertical line known as the Axis of Symmetry.
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
Based on the given information, answer the following questions:
(ii) The highway overpass is represented graphically. Zeros of a polynomial can be expressed graphically.
Number of zeros of polynomial is equal to which points?
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
Number of zeros of polynomial is equal to which points?
zero is 6 and sum of the zeros is 0
zero is 4 and sum of the zeros is 2
zero is 5 and sum of the zeros is 3
zero is 1 and sum of the zeros is 5
(2)
Highway Underpass whose one zero is 6 and sum of the zeros is 0, then write the polynomial.
Q 3
:
A highway underpass has a parabolic shape. A parabola is the graph that results from p(x) = ax² + bx + c. Parabolas are symmetric about a vertical line known as the Axis of Symmetry.
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
Based on the given information, answer the following questions:
(iii) (a) What is the shape of graph of a quadratic polynomial?
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
parabola
hyperbola
ellipse
circle
(1)
(a) Graph of a quadratic polynomial is always a parabola.
Q 4
:
A highway underpass has a parabolic shape. A parabola is the graph that results from p(x) = ax² + bx + c. Parabolas are symmetric about a vertical line known as the Axis of Symmetry.
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
Based on the given information, answer the following questions:
(iii) (b) Highway Underpass whose one zero is 6 and sum of the zeros is 0, then write the polynomial.
The Axis of Symmetry runs through the maximum or minimum point of the parabola, known as the vertex.
x² - 36
x² - 35
x² - 34
x² - 31
(2)
The zeros of the polynomial are 6 and -6.
So, the required polynomial is (x - 6)(x + 6) = x² - 36
Q 5
:
A graph of a cubic polynomial is plotted on a graph paper.
Based on the given information, answer the following questions:
(i) What is the sum of the zeros of the polynomial?
Based on the given information, answer the following questions:
-3
-2
-0
1
(3)
Zeros are the points where the graph cuts the x-axis, so from the graph, zeros are -5, 0 and 2.
∴ Sum of zeros = -3
Q 6
:
A graph of a cubic polynomial is plotted on a graph paper.
Based on the given information, answer the following questions:
(ii) The graph of given polynomial is extended on both sides. What does it indicate about the values of the y coordinate?
Based on the given information, answer the following questions:
-5
-3
2
-1
(2)
Values of the y coordinate will increase as we move right of 2 and continuously decrease as we move left of -5.
Q 7
:
Amit and Rahul decided to ride a new roller coaster. While waiting in line, Rahul notices that part of this roller coaster resembles the graph of a polynomial function that they have been studying in their maths class.
Based on the given information, answer the following questions:
(i) The brochure for the roller coaster says that, for the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t³ − 5t² + 21t, where t is the time in seconds and h is the height in feet. Classify this polynomial by degree and by number of terms.
3
2
1
0
(1)
We have polynomial h(t) = 0.3t³ − 5t² + 21t.
It is a degree 3 polynomial (cubic polynomial) having three terms (trinomial).
Q 8
:
Amit and Rahul decided to ride a new roller coaster. While waiting in line, Rahul notices that part of this roller coaster resembles the graph of a polynomial function that they have been studying in their maths class.
Based on the given information, answer the following questions:
(ii) Find the height of the roller coaster at t = 0 seconds. Explain why this answer makes sense.
at ground level
at upper level
at middle level
none of these
(1)
When t = 0 second:
h(0) = 0.3×0³ − 5×0² + 21×0 = 0
⇒ h = 0 feet when t = 0 second.
It means initially the coaster is at rest (at ground level).
Q 9
:
Amit and Rahul decided to ride a new roller coaster. While waiting in line, Rahul notices that part of this roller coaster resembles the graph of a polynomial function that they have been studying in their maths class.
Based on the given information, answer the following questions:
(iii) (a) Find the height of the roller coaster 9 seconds after the ride begins. Explain how you find the answer.
2.5 feet.
2.7 feet.
1.7 feet.
3.7 feet.
(2)
When t = 9 seconds:
h = 0.3×9³ − 5×9² + 21×9 = 218.7 − 405 + 189 = 2.7 feet.
Height after 9 seconds is 2.7 feet.
Q 10
:
Amit and Rahul decided to ride a new roller coaster. While waiting in line, Rahul notices that part of this roller coaster resembles the graph of a polynomial function that they have been studying in their maths class.
Based on the given information, answer the following questions:
(iii) (b) From the graph of the polynomial function for the height of the roller coaster, find the maximum height of the roller coaster.
25 feet.
22 feet.
15 feet.
19 feet.
(1)
Maximum height of the roller coaster = 25 feet.
