# CASE STUDY QUESTION 13-Class X-Maths

CASE STUDY QUESTION 13-Class X-Maths

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.

**(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

**Sol. **(i) Intersects x-axis

**(c) Graph of a quadratic polynomial is a**

(i) straight line

(ii) circle

(iii)parabola

(iv)ellipse

**Sol. ** (iii) parabola

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

(i) x^{2} – 6x + 2 (ii) x^{2} – 36 (iii) x^{2} – 6 (iv) x^{2} – 3

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

(i)1 (ii) 2 (iii) 0 (iv) 3