translation of quadratic equation.

Question

If the graph of a quadratic function y=3x²+2x+1 is translated two units horizontally and -3 units vertically, then we have the graph y=ax²+bx+c. Find the value of a+b+c.

Answer 1

Translating 2 units horizontally to the right gives y = 3(x-2)² + 2(x-2) +1

 

Translating 3 units downward we get y = 3(x-2)² + 2(x-2) + 1 - 3

 

                                                         = 3(x²-4x+4) +2x -6

 

                                                         = 3x² -10x + 6

 

So, a = 3, b = -10, c = 6

 

a+b+c = -1

 

Note:  If the horizontal translation is 2 units to the left, then instead of substituting x-2 for x, we would have substituted x+2 in place of x.