Mathematics, 30.01.2020 22:59, jacamron

Two functions are shown in the table below. function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 complete the table on your own paper, then select the value that is a solution to f(x) = g(x).

Answers: 3

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answered: damianb25

For $\fbox{\begin \\\math{x}=6\\\end{minispace}}$ the function $f(x)=-x^{2} +4x+12$ and g(x)=-x+6 has same value.

Step by step explanation:

The given functions are,

$f(x)=-x^{2}+4x+12$

g(x)=-x+6

Step 1:

Substitute x=1 in $f(x)=-x^{2} +4x+12$ to obtain the value of f(1) .

$f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15$

Substitute x=1 in g(x)=-x+6 to obtain the value of g(1) .

$g(1)=-1+6\\g(1)=5$

Step 2:

Substitute x=2 in $f(x)=-x^{2} +4x+12$ to obtain the value of f(2) .

$f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16$

Substitute x=2 in g(x)=-x+6 to obtain the value of g(2) .

$g(2)=-2+6\\g(2)=4$

Step 3:

Substitute x=3 in $f(x)=-x^{2} +4x+12$ to obtain the value of f(3) .

$f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15$

Substitute x=3 in g(x)=-x+6 to obtain the value of g(3) .

$g(3)=-3+6\\g(3)=3$

Step 4:

Substitute x=4 in $f(x)=-x^{2} +4x+12$ to obtain the value of f(4) .

$f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12$

Substitute x=4 in g(x)=-x+6 to obtain the value of g(4) .

$g(4)=-4+6\\g(4)=2$

Step 5:

Substitute x=5 in $f(x)=-x^{2} +4x+12$ to obtain the value of f(5) .

$f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7$

Substitute x=5 in g(x)=-x+6 to obtain the value of g(5) .

$g(5)=-5+6\\g(5)=1$

Step 6:

Substitute x=6 in $f(x)=-x^{2} +4x+12$ to obtain the value of f(6) .

$f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0$

Substitute x=6 in g(x)=-x+6 to obtain the value of g(6) .

$g(6)=-6+6\\g(6)=0$

Step 7:

As per the given condition f(x)=g(x) .

(a). Substitute $f(x)=-x^{2} +4x+12$ and g(x)=-x+6 in above equation.

$-x^{2} +4x+12=-x+6$

(b). Multiply with on both sides.

$x^{2} -4x-12=x-6$

(c). Shift the term x-6 to left hand side.

$x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0$

(d). Split the middle term in such a way that its sum is 5 and multiplication is 6.

$x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1 ,6$

It is observed from the above solution that for x=6 both the functions f(x) and g(x) has same value.

Direct method:

$f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1$

The table for the function $f(x)=-x^{2} +4x+12$ and g(x)=-x+6 is attached below.

Learn more:

1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. which is the graph of f(x) = (x – 1)(x + 4)?

Answer details:

Grade: Middle school.

Subjects: Mathematics.

Chapter: Function.

Keywords: Function, Middle term split method, Binomial,Quadratic, Polynomial, Factorized, Perfect square, Zeros, Zeros of a function, Expression, Equation, x, x^2, x^3, -x^2+4x+12, -x+6, roots of equation.

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

answered: ChiefRedCloud

The answer would be D.

Step-by-step explanation:

answered: Guest

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.
Which table shows a proportional relationship between x and y

Which table shows a proportional relationship between x and y

answered: Guest

This polygon has 4 sides
180(4-2) = 180(2) = 360 degree
80+90+2x + 3x = 360
170+5x = 360
5x = 190
x= 38
measure of angle t is 2(38)= 76
the answer is c. trust me
hope this !