Question

(09.01) 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. (put 1 or 2 in the blank space) (1 point)

Answer 1

Explanation:

Given are two functions and we have to find the maximum of those two

FIrst one is

`f(x) = -x^2+8x-15\\f(x) = -(x^2-8x+16-16)+15\\=-(x-4)^2 +31`

Thus we changed it into vertex form

Here since leading term is negative, parabola is open down and vertex is the maximum

Maximum = (4,15)

Second one is

`f(x) = -x^2+2x-15\\=-(x^2-2x+1-1)-15\\=-(x-1)^2 -14`

The above is into vertex form and also

Here since leading term is negative, parabola is open down and vertex is the maximum

Maximum = (1,-14)

Out of these two, y is greater for (4,15)

Hence I function has the larger maximum

Answer 2

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