Which equation has a graph that lies entirely above the x-axis?

A. y = - (x + 7) 2 + 7

B. y = (x - 7) 2 - 7

C. y = (x - 7) 2 + 7

D. y = (x - 7) 2

For the graph of a quadratic function to lie entirely above the x-axis, its leading coefficient (i. e. coefficient of x^2 must be positive so that the parabola representing the graph of the function will be facing up) and the vertex must be above x-axis (i. e. the y-value of the vertex that is k must be greater than 0). The equation of a quadratic function with vertex = (h, k) is given by (x - h) ^2 + k. For option A, the leading coeffitient is negative so the parabola will be facing down and hence will go below the x-axis. For option B, the vertex is given by (h, k) = (7, - 7), the y-value of the vertex is below the x-axis and hence some portion of the graph will fall below the x-axis. For option C, the vertex is given by (h, k) = (7, 7), the y-value of the vertex is above the x-axis and hence the graph will be entirely above the x-axis. For option D, the vertex is given by (h, k) = (7, 0), the y-value of the vertex is on the x-axis and hence the graph touches the x-axis. Therefore, the equation which graph is entirely abovr the x-axis is y = (x - 7) ^2 + 7 (option C).