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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)

Respuesta :

merlynthewhizz
Function 1 ⇒ [tex]f(x)=- x^{2} +8x-15[/tex]
Function 2 ⇒ [tex]- x^{2} +2x-15[/tex]

Both functions are shown in the graph below

As well as graphing, we can also find out the function with the highest maximum by using the formula to find the x-coordinate when the function is maximum/minimum

[tex]x=- \frac{b}{2a} [/tex]

Maximum vertex for function 1 is [tex]x=- \frac{8}{(2)(-1)} = \frac{-8}{-2} =4[/tex]
Maximum vertex for function 2 is [tex]x=- \frac{2}{(-2)(-1)}= \frac{-2}{-2}=1 [/tex]

Hence the function with the highest maximum is function 1
Ver imagen merlynthewhizz

Answer:

The Function __1__ has the larger maximum.

Step-by-step explanation:

The given functions are

Function 1:

[tex]f(x)=-x^2+8x-15[/tex]

Function 2:

[tex]f(x)=-x^2+2x-15[/tex]

Both functions are downward parabola because the leading coefficient is negative. So, the vertex is the point of maxima.

If a function is [tex]f(x)=ax^2+bx+c[/tex], then its vertex is

[tex]Vertex=(\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]

The vertex of Function 1 is

[tex]Vertex=(\frac{-8}{2(-1)}, f(\frac{-8}{2(-1)}))[/tex]

[tex]Vertex=(4, f(4))[/tex]

The value of f(4) is

[tex]f(4)=-(4)^2+8(4)-15=1[/tex]

The vertex of Function 1 is (4,1). Therefore the maximum value of Function 1 is 1.

The vertex of Function 2 is

[tex]Vertex=(\frac{-2}{2(-1)}, f(\frac{-2}{2(-1)}))[/tex]

[tex]Vertex=(1, f(1))[/tex]

The value of f(1)is

[tex]f(1)=-(1)^2+2(1)-15=-14[/tex]

The vertex of Function 2 is (1,-14). Therefore the maximum value of Function 2 is -14.

Since 1>-14, therefore Function __1__ has the larger maximum.

Ver imagen DelcieRiveria

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