Question

WILL MARK BRAINLIEST!!! PLZ HELP! The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 Function 2 f(x) = −x2 + 4x + 1 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (2, 5). Function 2 has the larger maximum at (3, 2).

Answer 1

Answer:

C

Step-by-step explanation:

The maximum/minimum values is simply the y-value of the vertex. Since both of the functions have a negative leading coefficient, they will both have maximum values.

For Function 1, we can see that the vertex is at (4,1). Thus, it's maximum value is at y=1.

For Function 2, we need to work out the vertex. To do this we can use:

$x=\frac{-b}{2a} ,y=f(-b/2a)$

To find the vertex.

Function 2 is defined by:

$f(x)=-x^2+4x+1$

Therefore:

$a=-1, b=4, c=1$

$x=-(4)/2(-1)=-4/-2=2\\f(2)=-(2)^2+4(2)+1\\=-4+8+1\\=4+1=5$

Thus, the vertex of Function 2 is at (2,5). Therefore, the maximum value of Function 2 is y=5.

5 is greater than 1, so the maximum value of Function 2 is greater.

The answer is choice C.