The equation of function h is h(x) = ½ (x-2)^2. The table shows some of the values of function m.

X : 8 | 10 | 12 | 14
m(x) : 2 | 3 | 4 | 5

Part A : What is the value of h(4) - m(16). Show your work or explain your answer.

Part B : If both of these functions are graphed on the same coordinate plane, how far apart are the y-intercepts? Explain how you obtained your answer.

Part C : For what values of x does m(x) exceed h(x)? Explain your answer.

Explanation:

1. Function h(x) (given)

2. Table with some values of the function m(x) (given)

x :          8    10    12    14

m(x):      2     3     4      5

Part A : What is the value of h(4) - m(16). Show your work or explain your answer.

To find m(16) you need to find the function m(x).

First, notice that it is a linear functio, because for constant increements of the input, x-values, there are constant increments of the output, m(x).

The point-slope equation of a linear function is:

Where m is the slope and x₁ and y₁ are the pair of coordinates of any point that belongs to the line.

Calculate m:

Use any two points. For instance (8,2), (10,3)

Replace m and any point into the point-slope equation:

Calculate h(4) and m(16)"

Part B : If both of these functions are graphed on the same coordinate plane, how far apart are the y-intercepts? Explain how you obtained your answer.

The y-intercepts are the values of y where the graph of the function crosses the y-axis.

That happens when x = 0.

Thus, to find the y-intercepts algebraically, you replace x with 0 in the equation of the function.

For h(x):

For m(x):

The distance is the absolute value of the difference:

Part C : For what values of x does m(x) exceed h(x)?

Subtract the functions and in for what values of x the difference is positive (greater than 0)

Check when that is greater than 0:

      Find the discriminant of the quadratic function:

Since the discriminant is negative, that equation never crosses the x-axis.

Then, it will always have the same sign.

Substitute x = 0:

Since 8 is greater than 0, you conclude that the left side is always greater than 0 and the inequality does not have solutions.

That means that m(x)never exceeds h(x).

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step-by-step explanation:

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