Question

Function 2

Answer 1

Answer:

Function 2 has larger max value.

Step-by-step explanation:

We know that the graph of Function 1 has the maximum value of 1 at x = 4 by looking at the graph.

But since we don't know what the maximum value of Function 2 is (Because Function 2 isn't given as a graph but rather an equation.) which means that we have to find the maximum value of Function 2.

$\large{f(x) = - {x}^{2} + 4x + 1}$

It is not necessary to find x-value for a function because we want to know which function has larger maximum value. We will be using the formula below.

$\large \boxed{y = \frac{4ac - {b}^{2} }{4a} }$

As you may know, a max-min value is indeed y-value. From Function 2, we know the value of a, b and c from standard form y = ax²+bx+c

Substitute our a, b and c in the formula.

$\large{y = \frac{4( - 1)(1) - {(4)}^{2} }{4( - 1)} } \\ \large{y = \frac{ - 4 - 16}{ - 4} } \\ \large{y = \frac{ - 20}{ - 4} = 5}$

Since our maximum value or y-value is 5 for Function 2. Since we also know that Function 1 has 1 as maximum value and Function 2 has 5 as maximum value. Therefore, Function 2 has larger maximum value.