Question

The equation of the function h is h... PLEASE HELP MATH

Answer 1

Answer:

Part A) $h(4) -m(16)=-4$

Part B) The distance between the y-intercepts is equal to 4 units

Part C) The value of h(x) will always be greater than the value of m(x) for any value of x

Step-by-step explanation:

Part A) What is the value of h(4) -m(16)

we have

$h(x)=\frac{1}{2}(x-2)^2$

For x=4

$h(4)=\frac{1}{2}(4-2)^2=2$

Find the equation of the line m(x)

Find the slope

take the points

(8,2) and (12,4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{4-2}{12-8}$

$m=\frac{2}{4}$

$m=\frac{1}{2}$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=\frac{1}{2}$

$point\ (8,2)$

substitute

$2=\frac{1}{2}(8)+b$

solve for b

$b=-2$

$y=\frac{1}{2}x-2$

therefore

$m(x)=\frac{1}{2}x-2$

Find m(16)

$m(16)=\frac{1}{2}(16)-2=6$

so

$h(4) -m(16)=2-6=-4$

Part B) we know that

The y-intercept is the value of y when the value of x is equal to zero

Find the y-intercept of h(x)

For x=0

$h(0)=\frac{1}{2}(0-2)^2=2$

Find the y-intercept of m(x)

For x=0

$m(0)=\frac{1}{2}(0)-2=-2$

therefore

The distance between the y-intercepts is equal to 2-(-2)=4 units

Part C)

Graph both equations

$h(x)=\frac{1}{2}(x-2)^2$

$m(x)=\frac{1}{2}x-2$

using a graphing tool

see the attached figure

The value of h(x) will always be greater than the value of m(x) for any value of x