Question

Transform the quadratic function defined by y=ax2+bx+c into the form y=a(x-h)2+k 1.Y=x2-6x-3 2.Y=5x2-20x-5

Answer 1

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