Final answer:
To transform the parabola y=x^2 by shifting it up by 7 units and to the left by 1 unit, the new equation becomes y=(x+1)^2+7.
Step-by-step explanation:
The student has asked about transforming the equations of parabolas, which is a topic in algebra and precalculus. The specific transformation involves shifting the graph of the parabola y = x^2 up by 7 units and to the left by 1 unit. To achieve this transformation, we adjust the original equation to reflect these changes.
In general, shifting a parabola up by 'k' units adds 'k' to the y-value of every point, and shifting it to the left by 'h' units subtracts 'h' from the x-value of every point in the original graph. Consequently, the equation of the transformed parabola becomes y = (x + 1)^2 + 7.