Give the equation of the function whose graph is described.

Question

The graph of y = x^2 is shifted 4 units to the right. This graph is then vertically stretched by a factor of 5 and reflected across the x-axis. Finally, the graph is shifted 8 units upward.

Answer 1

y = x²

 

To shift 4 units to the right, replace x with (x-4).  (To shift left, replace x with (x+4))

 

    y = (x-4)²

 

To stretch vertically by a factor of 5, multiply (x-4) by 5

 

    y = 5(x-4)²

 

To reflect across the x-axis, change the sign of 5

 

    y = -5(x-4)²

 

To shift up by 8, simply add 8 to the expression:

 

    y = -5(x-4)² + 8

 

Finally, multiply out the term -5(x-4)² and simplify to get the answer.