Question

5. A curve has equation y = 10x –x^2.
A) Express 10x –x^2 in the form a - (x +b)^2 .

Answer 1

SOLUTION

GIVEN

A curve has equation

$\sf{y = 10x - {x}^{2} }$

TO EXPRESS

$\sf{10x - {x}^{2} \: \: \: in \: the \: form \: \: a - {(x + b)}^{2} }$

EVALUATION

Here the given equation of curve is

$\sf{y = 10x - {x}^{2} }$

We rewrite it as below

$\sf{y = 10x - {x}^{2} }$

$\sf{ = - ( {x}^{2} - 10x) }$

$\sf{ = - ( {x}^{2} - 2.x.5 + {5}^{2} - {5}^{2} ) }$

$\sf{ = {5}^{2} - ( {x}^{2} - 2.x.5 + {5}^{2} ) }$

$\sf{ = 25 - {(x - 5)}^{2} }$

Which is of the form

$\sf{ a - {(x + b)}^{2} \: \: \: where \: \: a = 25 \: \: and \: b \: = - 5}$

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