Question

Use the functions f(x) and g(x) to determine which function has the largest zero and provide its coordinates. f(x) = 4x2 − 16x + 16
x g(x)
18 −17
19 0
20 19
21 40
22 63

f(x); (−2, 0)
f(x); (2, 0)
g(x); (19, 0)
g(x); (63, 0)

Answer 1

Answer:

The function that has the largest zero is g(x) and its coordinates are (19,0)

Step-by-step explanation:

we know that

The zeros of the function (or x-intercepts) are the values of x when the value of the function is equal to zero

we have

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

Find the x-intercepts of f(x)

Equate f(x) to zero

$4x^{2}-16x+16=0$

Complete the square

$4(x^{2}-4x)=-16$

$4(x^{2}-4x+4)=-16+16$

$4(x^{2}-4x+4)=0$

$4(x-2)^{2}=0$

$x=2$ -----root with a multiplicity of 2

therefore

The x-intercept of f(x) is the point (2,0)

Find the x-intercept of g(x)

Observing the table

For g(x)=0, x=19

therefore

The x-intercept of g(x) is the point (19,0)

Compare the zeros of f(x) and g(x)

The function that has the largest zero is g(x) and its coordinates are (19,0)

Answer 2

Answer:

g(x); (19,0)

Step-by-step explanation:

The zeros are the x values where the graph intersects the x-axis. To find zeros replace y with 0 and solve for x.

f(x) = (2,0)