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Maths Case study (4 Marks)

Quadratic Equations · Jharkhand Board (JAC) STD 10 (Jharkhand - English Medium). 5 questions.

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Case study (4 Marks)

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5 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks

Applications‌ ‌of‌ ‌Parabola‌ - Suspension‌ Bridge
If‌ ‌the‌ ‌road‌ ‌the‌ ‌roadway‌ ‌of‌ ‌a‌ ‌suspension‌ ‌bridge‌ ‌is‌ ‌loaded‌ ‌uniformly par‌ ‌horizontal meter,‌ ‌the‌ ‌suspension‌ ‌cable‌ ‌hangs‌ ‌in‌ ‌the‌ ‌form‌ ‌of‌ ‌arc‌ ‌which‌ ‌closely‌ ‌approximate‌ ‌to‌ parabolic‌ ‌arcs.‌ ‌Therefore,‌ ‌parabolic‌ ‌arcs‌ ‌are‌ ‌used‌ ‌in‌ ‌suspension‌ cable‌ ‌bridge‌ ‌construction.‌
‌Parabola:‌ ‌A‌ ‌parabola‌ ‌is‌ ‌the‌ ‌graph‌ ‌that‌ ‌results from $px(x) = ax^2 + bx + c$. Parabola‌ are symmetric ‌about‌ ‌a‌ ‌vertical‌ ‌line‌ ‌known‌ ‌as‌ ‌the‌ ‌Axis‌ ‌of‌ ‌symmetry.
  1. Find the number of polynomial having zeroes as 1 and -2.
  2. Graph of quadratic polynomial is a:
  3. If the susnension cable of a bridge hangs in the form of arcs is represented by $4x^2- 20x + 9,$ then its zerores are:
    Or
    The number of zeroes that polynomial $p(x) = x^3 - 4x$ can have is:
Answer
1. More than 32. Parabola.
3. $\Big(\frac12,\frac92\Big)$
Or
3
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Question 24 Marks

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.
  1. 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:
  2. Graph of a quadratic polynomial is a:
  3. The representation of Highway Underpass whose one zero is 10 and sum of the zeroes is 16, is:
    Or
    The number of zeroes that polynomial $f(x) = (x - 3)^2 + 1$ can have is:
Answer
1. Intersects x-axis2. Parabola
$3.x^2 - 16x + 60$
Or
0
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Question 34 Marks

Applications of Parabolas
Parabola has many applications in our day-to-day life. For example, if an object (projectile) is thrown in space, then the path of the projectile is a parabola. If we know the equation of the path of a projectile by using various properties of parabola, we can obtain may important results like greatest height attained by the projectile, its horizontal range reached etc.
Parabola: A parabola is the graph that results from $p(x) = ax^2 + bx + c$ they are symmetric about a vertical line known as the axis of symmetry and runs through the maximum or minimum point of the parabola which is called the vertex.

Graph of a quadratic polynomial is:
The number of zeroes that polynomial $p(x)=(x-2)^2+5$ can have is:
If a parabolic trajectory is represented by $x^2-4 x+3$, then its zeroes are:
Or
If one zero of a parabolic trajectory $p(y)=5 y^2-14 y+k$ is reciprocal of the other, the find the value of $k$ :
Answer
1. Parabolic2. 0
3. (1, 3)
Or
5
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Question 44 Marks

A highway underpass a 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.
  1. Graph of a quadratic polynomial is ?
  2. The highway overpass is represented graphically. Zeroes of the polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of the polynomial ?
  3. If the highway overpass is represented by $x^2 + 2x - 15,$ then its zeroes are ?
    Or
    The number of zeroes for the polynomial $\text{y} = \text{g(x)} = (\text{x} + 3) (\text{x} - 1) - 3\Big(\text{x}-\frac13\Big)$ is ?
Answer
1. Parabola2. Parabola
3. (3, -5)
Or
2
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Question 54 Marks

Applications‌ ‌of‌ ‌Parabola‌ - Suspension‌ Bridge
If‌ ‌the‌ ‌road‌ ‌the‌ ‌roadway‌ ‌of‌ ‌a‌ ‌suspension‌ ‌bridge‌ ‌is‌ ‌loaded‌ ‌uniformly par‌ ‌horizontal meter,‌ ‌the‌ ‌suspension‌ ‌cable‌ ‌hangs‌ ‌in‌ ‌the‌ ‌form‌ ‌of‌ ‌arc‌ ‌which‌ ‌closely‌ ‌approximate‌ ‌to‌ parabolic‌ ‌arcs.‌ ‌Therefore,‌ ‌parabolic‌ ‌arcs‌ ‌are‌ ‌used‌ ‌in‌ ‌suspension‌ cable‌ ‌bridge‌ ‌construction.‌
‌Parabola:‌ ‌A‌ ‌parabola‌ ‌is‌ ‌the‌ ‌graph‌ ‌that‌ ‌results from $px(x) = ax^2 + bx + c$. Parabola‌ are symmetric ‌about‌ ‌a‌ ‌vertical‌ ‌line‌ ‌known‌ ‌as‌ ‌the‌ ‌Axis‌ ‌of‌ ‌symmetry.
  1. Find the number of polynomials having zeroes as 0 and -3:
  2. Graph of a quadratic polynomial is a:
  3. If the suspension cable of a bridge hangs in the form of arcs is represented by $x^2 - 9x + 8$, then its zeroes are:
    Or
    Find a quadratic polynomials whose are 2 and 5:
Answer
1. More than 32. Parabola.
3. (1, 8)
Or
$x^2 - 7x + 10$
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