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Answer:
1) y = (x-3)²-12
2) y = 5(x-2)²-9
Step-by-step explanation:
Given the quadratic expressions
y=x²-6x-3
We are to transform it in the form y=ax²+bx+c
y=(x²-6x)-3
Complete the square of the expression in parenthesis
y = (x²-6x + (6/2)² - (6/2)²)-3
y = (x²-6x+3²-3²)-3
y = (x²-6x+9-9)-3
y = (x²-6x+9)-12
y = (x²-3x-3x+9)-12
y = x(x-3)-3(x-3)-12
y = (x-3)(x-3)-12
y = (x-3)²-12
Hence the transformation is y = (x-3)²-12 where a = 1 and k = -12
For the quadratic equation
y=(5x²-20x)-5
y = 5(x²-4x)- 5
Complete the square of the expression in parenthesis
y = 5(x²-4x+4-4)- 5
y = 5(x²-4x+4)-9
y = 5(x-2)²-9
Hence the transformation is y = 5(x-2)²-9 where a = 5 and k = -9