What is y=x^2+74, translated 2 units up and 5 units left

y = x² + 10x + 101

Step-by-step explanation:

Start with the basic function: y = x² + 74.

To shift the parabola up two units, you add two units to the value of y. The equation becomes

y = x² + 76

To shift the parabola five units to the left, you must add five units to the value of x. The equation for the parabola becomes

y = (x + 5) ² + 76

y = x² + 10x + 25 + 76

y = x² + 10x + 101

The figure below shows the graphs of

y = x² (red)

y = x² + 76 (blue) (shifted up two units)

y = x² + 10x + 101 (green) (shifted left five units)

There's an answer

y = (x+5) ^2+76