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Function 2

+ 4x + 1
Function _
has the larger maximum.
(Put 1 or 2 in the blank space)

Function 2 + 4x + 1 Function _ has the larger maximum. (Put 1 or 2 in the blank space-example-1
User Polyvertex
by
8.4k points

1 Answer

6 votes

Answer:

Function 2 has larger max value.

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 = ( - 4 - 16)/( - 4) } \\ \large{y = ( - 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.

User Skarllot
by
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