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


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


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