Question

16.
Read the case study carefully and answer any four out of the following questions:
A car moves on a highway, the path trace by the car is shown below.
The pattern of the path traced in the shape of parabolic in mathematical form, the given path
followed the polynomial expression in the form
pela - Txin-1 at 2n 2).
i. In the equation ax2.hxc. if curve passes through (0,0).(-3.-4), (3, 4) then the value of a b
and is
a ao co
b. a = 0.1 0.
cabo.co
b. o

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

In the equation ax² + bx + c , if curve passes through (0,0), (-3,-4), (3,-4) then the value of a, b and c is

$\displaystyle\sf{a. \: \: \: \: \: a = 0,b = c = 0}$

$\displaystyle\sf{b. \: \: \: \: \: a = 0,b = 0,c = - \frac{4}{9} }$

$\displaystyle\sf{c. \: \: \: \: \: a = - \frac{4}{9} ,b = 0,c = 0 }$

$\displaystyle\sf{d. \: \: \: \: \: a = - \frac{4}{9} ,b = 0,c = - \frac{4}{9} }$

EVALUATION

Here the given equation is ax² + bx + c

$\displaystyle\sf{ Let \: \: y = a {x}^{2} + bx + c \: \: \: - - - (1)}$

Equation 1 passes through the point (0,0)

Thus we get

$\displaystyle\sf{ 0 = a. {0}^{2} + b.0 + c \: \: \: }$

$\displaystyle\sf{ \implies \: c = 0 \: \: \: }$

So the Equation 1 becomes

$\displaystyle\sf{ y = a {x}^{2} + bx \: \: \: - - - (2)}$

Now Equation 2 passes through the point (-3,-4)

So we get

$\displaystyle\sf{ - 4 = a .{( - 3)}^{2} + b.( - 3) \: \: \: }$

$\displaystyle\sf{ \implies \: 9 a - 3 b = - 4 \: \: \: - - - (3)}$

Again Equation 2 passes through the point (3,-4)

So we get

$\displaystyle\sf{ - 4 = a .{( 3)}^{2} + b.( 3) \: \: \: }$

$\displaystyle\sf{ \implies \: 9 a + 3 b = - 4 \: \: \: - - - (4)}$

Subtracting Equation 3 from Equation 4 we get

$\displaystyle\sf{ \implies \: 6 b = 0}$

$\displaystyle\sf{ \implies \: b = 0}$

Putting the value of b in Equation 4 we get

$\displaystyle\sf{ 9a = - 4}$

$\displaystyle\sf{ \implies \:a = - \frac{4}{9} }$

Thus we get

$\displaystyle\sf{ \: a = - \frac{4}{9} ,b = 0,c = 0 }$

FINAL ANSWER

Hence the correct option is

$\displaystyle\sf{c. \: \: \: \: \: a = - \frac{4}{9} ,b = 0,c = 0 }$

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