Topic Question Set
Q 11
:
Basketball and soccer are both played with a spherical ball. Although athletes dribble the ball in both sports, a basketball player uses their hands, while a soccer player uses their feet. of both the soccer ball and the basketball forms a parabola, representing a quadratic polynomial.
Based on the given information, answer the following questions:
(i) The shape of the path traced shown is?
parabola
hyperbola
ellipse
circle
(1)
Shape of the path traced is a parabola.
Q 12
:
Basketball and soccer are both played with a spherical ball. Although athletes dribble the ball in both sports, a basketball player uses their hands, while a soccer player uses their feet. of both the soccer ball and the basketball forms a parabola, representing a quadratic polynomial.
Based on the given information, answer the following questions:
(ii) For polynomial p(x) = ax² + bx + c, if the graph of the parabola opens upward, a will be?
a > 1
a > 0
a < 0
a > 2
(2)
a will be positive if the graph of the parabola opens upwards, i.e., a > 0
Q 13
:
Basketball and soccer are both played with a spherical ball. Although athletes dribble the ball in both sports, a basketball player uses their hands, while a soccer player uses their feet. of both the soccer ball and the basketball forms a parabola, representing a quadratic polynomial.
Based on the given information, answer the following questions:
(iii) Observe the following graph and answer:
(a) In the above graph, how many zeros are there for the polynomial?
(a) In the above graph, how many zeros are there for the polynomial?
three zeros
four zeros
two zeros
one zeros
(1)
The graph crosses the x-axis three times, so there are three zeros.
Q 14
:
Basketball and soccer are both played with a spherical ball. Although athletes dribble the ball in both sports, a basketball player uses their hands, while a soccer player uses their feet. of both the soccer ball and the basketball forms a parabola, representing a quadratic polynomial.
Based on the given information, answer the following questions:
(iii) Observe the following graph and answer:
(b) What will be the expression of the polynomial?
(b) What will be the expression of the polynomial?
k ≠ 0
k ≠1
k ≠ 2
k ≠ - 0
(1)
From the graph, zeros of the polynomial are −3, −1, and 2.
Expression of the polynomial will be: f(x) = k(x − (−3))(x − (−1))(x − 2)
= k(x + 3)(x + 1)(x − 2)
= k(x³ + 2x² − 5x − 6), where k ≠ 0.
