CASE STUDY 3:
Basketball and soccer are played with a spherical ball. Even though an athlete
dribbles the ball in both sports, a basketball player uses his hands and
a soccer player uses his feet. Usually, soccer is played outdoors on a large field
and basketball is played indoor on a court made out of wood. The projectile (path
traced) of soccer ball and basketball are in the form of parabola representing
quadratic polynomial.
1. The shape of the path traced shown is
a) Spiral
b) Elipse
c) Linear
d) Parabola
2. The graph of parabola opens upwards
a) a=0
b) a < 0
c) a > 0
d) a 20
3. Observe the following graph and answer
Answers
32) (a) The shape of the path traced shown is :-
a) Spiral
b) Ellipse
c) Linear
d) Parabola
Answer :- d) Parabola .
32) (b) The graph of parabola opens upwards, if _______ *
a) a = 0
b) a < 0
c) a > 0
d) a ≥ 0
Answer :-
- c) a > 0 .
- if asked downward it will be a < 0 .
32) (c) Observe the following graph and answer. In the given graph, how many zeroes are there for the polynomial ?
a) 0
b) 1
c) 2
d) 3
Answer :- d) 3
As we can see that, the graph is cutting x - axis 3 times . so, we can conclude that, there are 3 zeroes for the polynomial .
32) (d) The three zeroes in the above shown graph are :-
a) 2, 3,-1
b) -2, 3, 1
c) -3, -1, 2
d) -2, -3, -1
Answer :-
- The graph is cutting at :- (-3), (-1), and 2 . (c)
32) (e) What will be the expression of the polynomial ?
a) x³ + 2x² – 5x – 6
b) x³ + 2x² – 5x + 6
c) x³ + 2x² + 5x – 6
d) x³ + 2x² + 5x + 6
Answer :-
we have, three roots as ,
- a = (-3)
- b = (-1)
- c = 2
so,
→ Required polynomial = x³ - (a + b + c)x² + (ab + bc + ca)x - abc = 0
putting values we get,
→ Required polynomial = x³ - (-3 - 1 + 2)x² + (-3*-1 - 1*2 - 3*2)x - (-3)*(-1)*2
→ Required polynomial = x³ + 2x² - 5x - 6 (a) .
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