Question

please help me answer this
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Answer 1

Given :

• quadratic equations in form of y = ax² + bx + c

To find :

• y = a×(x-h)² + k , form of given equation.

Method used :

• we have to make given equation a perfect square by adding and subtracting the same number

Solution :

1) y = x² - 6x - 3

=> y = x² - 2(x)×3 - 3

{ add and subtract (3)² on RHS }

=> y = x² - 2(x)(3) + (3)² - (3)² -3

=> y = ( x² - 2(3)(x) + 9 ) - 9 - 3

=> y = 1×(x-3)² - 12

• on comparison , h = 3 k = (-12)

2) y = 5x² - 20x -5

=> y = 5(x² - 4x) - 5

=> y = 5{x² - 2(x)(2)} - 5

{add and subtract (2)² on RHS}

=> y = 5 { x² - 2(x)(2) + (2)² - (2)² } -5

=> y = 5{ (x² - 2(x)(2) + 2² ) - 4 } - 5

=> y = 5× (x-2)² - 5(4) - 5

=> y = 5×(x-2)² - 20 - 5

=> y = 5×(x-2)² - 25

• on comparison , h = 2 k = (-25)

ANSWER :

1) y = 1×(x-3)² - 12

2) y = 5×(x-2)² - 25