Applications of Parabolas: Highway Overpasses/  Underpasses  A highway underpass is parabolic in shape.

Parabola A parabola is the graph that results from p(x) = ax 2 + 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.

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Question 1

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

(a) (2, – 4)  

(b) (4, – 2)

(c) (– 2, – 2)  

(d) (– 4, – 4)

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Question 2

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:

(a) Intersects X-axis

(b) Intersects Y-axis

(c) Intersects Y-axis or X-axis

(d) None of the above

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Question 3

Graph of a quadratic polynomial is a:

(a) straight line  

(b) circle

(c) parabola  

(d) ellipse

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Question 4

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

(a) x 2 – 6x + 2  

(b) x 2 – 36

(c) x 2 – 6 

(d) x 2 – 3

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Question 5

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

(a) 1  

(b) 2

(c) 0  

(d) 3

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Question Applications of Parabolas: Highway Overpasses/ Underpasses A highway underpass is parabolic in shape. Shape of Cross Slope: 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. Question 1 If the highway overpass is represented by x2 – 2x – 8. Then its zeroes are (a) (2, – 4) (b) (4, – 2) (c) (– 2, – 2) (d) (– 4, – 4) Finding Zeroes of polynomial x2 – 2x – 8 = 0 Using splitting the middle term x2 – 4x + 2x – 8 = 0 x(x – 4) + 2(x – 4) = 0 (x – 4) (x + 2) = 0 ∴ x = 4, x = –2 So, the correct answer is (B) Question 2 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: (a) Intersects X-axis (b) Intersects Y-axis (c) Intersects Y-axis or X-axis (d) None of the above We know that Number of zeroes is equal to number of times parabola intersects the x-axis So, the correct answer is (A) Question 3 Graph of a quadratic polynomial is a: (a) straight line (b) circle (c) parabola (d) ellipse Graph of a quadratic polynomial is a parabola. So, the correct answer is (C) Question 4 The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is: (a) x2 – 6x + 2 (b) x2 – 36 (c) x2 – 6 (d) x2 – 3 Given a polynomial where One Zero = 𝛼 = 6 And, Sum of zeroes = 0 𝛼 + 𝛽 = 0 6 + 𝛽 = 0 𝛽 = −6 Since zeroes of polynomial are 6 and −6 Our quadratic polynomial is (x − 6) (x − (−6)) (x − 6) (x + 6) x2 − 62 x2 − 36 So, the correct answer is (B) Question 5 The number of zeroes that polynomial f(x) = (x – 2)2 + 4 can have is: (a) 1 (b) 2 (c) 0 (d) 3 Given f(x) = (x – 2)2 + 4 = x2 + 4 – 4x + 4 = x2 – 4x + 8 Finding Zeros of f(x) x2 – 4x + 8 Using quadratic formula a = 1, b = −4, c = 8 Finding D D = b2 −4ac = (−4)2 − 4 × 1 × 8 = 16 − 32 = −16 Since D < 0 It has no real roots Thus, f(x) does not have any zeroes ∴ Number of zeroes of f(x) = 0 So, the correct answer is (C)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.