Case Study Based- 3

Applications of Parabolas-Highway Overpasses/Underpasses

A highway underpass is parabolic in shape.

Parabola

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 which is called the Vertex

(a) If the highway overpass is represented by x² – 2x – 8. Then its zeroes are

(i) (2,-4) (ii) (4,-2) (iii) (-2,-2) (iv) (-4,-4)

(b) The highway overpass is represented graphically.

Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial

(i) Intersects x-axis

(ii) Intersects y-axis

(iii) Intersects y-axis or x-axis

(iv)None of the above

(c) Graph of a quadratic polynomial is a

(i) straight line

(ii) circle

(iii)parabola

(iv)ellipse

(d) The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is

(i) x² – 6x + 2

(ii) x² – 36

(iii)x² – 6

(iv)x² – 3

(e) The number of real zeroes that polynomial f(x) = (x – 2)² + 4 can have is:

(i)1

(ii) 2

(iii) 0

(iv) 3

Find the probability of getting a doublet in a throw of a pair of dice.

OR

Find the probability of getting a black queen when a card is drawn at random from a well-shuffled pack of 52 cards.

Case Study based-1

SUN ROOM

The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using

• Four clear glass panels, trapezium in shape, all the same size

• One tinted glass panel, half a regular octagon in shape

(a) Refer to Top View

Find the mid-point of the segment joining the points J (6, 17) and I (9, 16).

(i) (33/2,15/2)

(ii) (3/2,1/2)

(iii)(15/2,33/2)

(iv) (1/2,3/2)

(b) Refer to Top View

The distance of the point P from the y-axis is

(i) 4 (ii) 15 (iii) 19 (iv) 25

(c) Refer to Front View

The distance between the points A and S is

(i) 4 (ii) 8 (iii)16 (iv)20

(d) Refer to Front View

Find the co-ordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally.

(i) (8.5,2.0) (ii) (2.0,9.5) (iii) (3.0,7.5) (iv) (2.0,8.5)

(e) Refer to Front View

If a point (x,y) is equidistant from the Q(9,8) and S(17,8),then

(i) x+y=13 (ii) x-13=0 (iii) y-13=0 (iv)x-y=13

3 bells ring at an interval of 4,7 and 14 minutes. All three bell rang at 6 am, when the three balls will the ring together next?

Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2).

OR

P (-2, 5) and Q (3, 2) are two points. Find the co-ordinates of the point R on PQ such that PR=2QR.