# Two functions are shown in the table below. function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2

###### Question:

function 1 2 3 4 5 6

f(x) = −x2 + 4x + 12

g(x) = x + 2

complete the table on your own paper, then select the value that is a solution to f(x) = g(x).

x = 2

x = 3

x = 5

x = 6

## Answers

Its x=3

i just took the test

hope this helps

F(x)=-x^2+4x+12, g(x)=x+2, If there is a solution y=y, f(x)=g(x) so we can say:

-x^2+4x+12=x+2

x^2-3x-10=0

x^2-5x+2x-10=0

x(x-5)+2(x-5)=0

(x+2)(x-5)=0, so there are two solutions to the system of equations when x=-2 and 5, now find the corresponding y values given y=x+2

y(-2)=-2+2=0 and y(5)=5+2=7 so the two solutions are the two points:

(-2,0) and (5,7)

The correct answer is x=5

Step-by-step explanation:

D) 6

Step-by-step explanation:

Step-by-step explanation:

Here are the values of each function. To get the value, just replace x with the given number

[tex]f(x) =-x^2+4x+12[/tex]

f(1)=15, f(2) = 16,f(3) = 15,f(4) =12, f(5) =7, f(6) =0

[tex]g(x)=x+2[/tex]

g(1) = 3, g(2) = 4, g(3) = 5, g(4) = 6, g(5) = 7, g(6) = 8

So, note that at x=5, f(x) = g(x) = 7

The correct option is x = 5

Please find the attached graph of the function

Step-by-step explanation:

The given functions are;

1) f(x) = -x² + 4·x + 12

2) g(x) = x + 2

The table of values are therefore;

x, f(x), g(x)

-7, -65, -5

-6, -48, -4

-5, -33, -3

-4, -20, -2

-3, -9, -1

-2, 0, 0

-1, 7, 1

0, 12, 2

1, 15, 3

2, 16, 4

3, 15, 5

4, 12, 6

5, 7, 7

6, 0, 8

Therefore the solution to the equation f(x) = g(x), occurs at x = -2 and x = 5, where f(x) = g(x) = 0 and 7 respectively

To verify, we have;

Equating the two functions gives;

f(x) = g(x)

-x² + 4·x + 12 = x + 2

-x² + 4·x + 12 - (x + 2) = 0

-x² + 3·x + 10 = 0

(x + 2)(x - 5) = 0

x = 5 or -2

The correct option is x = 5.

[tex]Two functions are shown in the table below: Function 1 2 3 4 5 6 f(x) = -x2 + 4x + 12 g(x) = x + 2[/tex]

The other person that has commented on this made the explanation seem difficult but they were correct. I just had the same question and the answer is x=5

Step-by-step explanation:

x = 5

I think it is this answer becuase when x = 5 y = 7 for both the equations

I did the math and put it on the table below.

I hope you have a good day, and I hope this is right, if not I will try and fix it!

[tex]PLEASE HELPP! Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12[/tex]

x f(x) g(x)

1 15 3

2 16 4

3 15 5

4 12 6

5 7 7

6 0 8

f(x) = g(x) when x = 5

Step-by-step explanation:

f(x) = -x² + 4x + 12

f(1) = -(1)² + 4(1) + 12 = 15

f(2) = -(2)² + 4(2) + 12 = 16

f(3) = -(3)² + 4(3) + 12 = 15

f(4) = -(4)² + 4(4) + 12 = 12

f(5) = -(5)² + 4(5) + 12 = 7

f(6) = -(6)² + 4(6) + 12 = 0

g(x) = x + 2

g(1) = 1 + 2 = 3

g(2) = 2 + 2 = 4

g(3) = 3 + 2 = 5

g(4) = 4 + 2 = 6

g(5) = 5 + 2 = 7

g(6) = 6 + 2 = 8

This can be done in two ways

One method is to check the answer options in both f(x) and g(x) and select the one that matches for both.

The second is to form a quadratic equation and solving as such:

f(x) = g(x)

-x² + 4x + 12 = x + 8

x² - 3x - 4 = 0

(x - 4)(x + 1) = 0

x = 4; x = -1

Only x = 4 is given in the options, so the answer is B