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While playing badminton Ravi has set the barrier chain hung between two posts at the edge of the walkway of a street. It is hung in the shape of a parabola.
Based on the above information answer the following questions :
(a) Which type of the polynomial (linear, quadratic, cubic etc.) is graphically represented by a parabola ?
(b) If the polynomial represented by a parabola, intersects the $x$-axis at $-2$ and $3$ and $y$-axis at $-3$, then write the zeroes of the parabola.
(c) Find the expression for the above polynomial.
OR
(c) If the zeroes of the polynomial are $-5$ and $3$, find its expression.
Based on the above information answer the following questions :
(a) Which type of the polynomial (linear, quadratic, cubic etc.) is graphically represented by a parabola ?
(b) If the polynomial represented by a parabola, intersects the $x$-axis at $-2$ and $3$ and $y$-axis at $-3$, then write the zeroes of the parabola.
(c) Find the expression for the above polynomial.
OR
(c) If the zeroes of the polynomial are $-5$ and $3$, find its expression.
Show SolutionHide Solution↓
(a) Quadratic (1 Mark)
(b) $-2$ and $3$ (1 Mark)
(c) $p(x) = k(x + 2)(x - 3)$ (1 Mark)
$p(x) = k(x^2 - x - 6)$
Using point $(0, -3)$, $-3 = k(0 - 0 - 6) \Rightarrow k = \frac{1}{2}$
$p(x) = \frac{1}{2}(x^2 - x - 6)$ (1 Mark)
OR
(c) $g(x) = (x + 5)(x - 3)$ (1 Mark)
$g(x) = x^2 + 2x - 15$ (1 Mark)
(b) $-2$ and $3$ (1 Mark)
(c) $p(x) = k(x + 2)(x - 3)$ (1 Mark)
$p(x) = k(x^2 - x - 6)$
Using point $(0, -3)$, $-3 = k(0 - 0 - 6) \Rightarrow k = \frac{1}{2}$
$p(x) = \frac{1}{2}(x^2 - x - 6)$ (1 Mark)
OR
(c) $g(x) = (x + 5)(x - 3)$ (1 Mark)
$g(x) = x^2 + 2x - 15$ (1 Mark)