Question

the following graph describes function 1, and the equation below it describes function 2: function 1 graph of function f of x equals negative x squared plus 8 multiplied by x minus 15 function 2 f(x) = −x2 2x − 15 function has the larger maximum.

Answer 1

function 1: f(x) = -x^2 + 8x - 15 = -(x^2 - 8x + 15) = -(x^2 - 8x + 16 + 15 - 16) = -(x - 4)^2 + 1
Vertex = (4, 1)
function 2: f(x) = -x^2 + 2x - 15 = -(x^2 - 2x + 15) = -(x^2 - 2x + 1 + 15 - 1) = -(x - 1)^2 - 14
vertex = (1, -14)
Larger maximum is f(x) = -x^2 + 8x - 15