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)=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.

(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) x² – 6x + 2 (ii) x² – 36 (iii) x² – 6 (iv) x² – 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