The flight path of a spacecraft is represented by the parabola y = x^2. If the engine is shut down at the point P (a, a^2), the spaceship will fly off along the tangent line at P. If the spaceship is moving from left to right, at what point should the engine be shut down in order for the spacecraft to move through point (4, 7)?

Hint: you need to set up an equation for the slope of the straight line that passes through points (a,a^2) and (4,7), and set it equal to the slope of the parabola at point a, then solve for a. Post back with what you get for an answer, or if you're stuck show us your work and we'll give a pointer or two.

Thank You! Got it!