The graph of y = -5(x-4)^2+7 can be obtained from the graph of y = x^2 by shifting horizontally__ units to the____, vertically stretching by a factor of___, reflecting across the__-axis, and shifting vertically__ units in the_____direction.

Shift a function left along the x-axis by adding the number of spaces to be shifted to x. Subtract if you wish to shift to the right; e.g. to shift x^{2} 2 spaces to the left, change x^{2} to (x+2)^{2}

To stretch in the y-direction, multiply all terms in the equation by the factor to be stretched; e.g. to stretch y = 2x - 3 by a factor of 2, y = 4x - 6

To reflect across the x-axis, change the signs; e.g. y = 2x - 3 becomes y = -2x + 3

To shift up vertically, merely add the number of spaces to be moved; e.g. to shift up 4 spaces, y = 2x - 3 becomes y = 2x +1. Subtract to shift down.