The graph of h is a translation 6 units down and 2 units left of the graph of f(x)=x^2−7x. For each value of x, g(x) is 115% of h(x). Write a rule for g. g(x)=

Answer 1

We start with f(x)=x²-7x

The get the graph of h, we translate f(x) 6 units down and 2 units left.

Let's translate it 6 units down first. This gives us f(x)= x²-7x-6

Next, let's translate it 2 units left. This means that each x value will be moved to units to the left, so we can think of it as each x in our equation being affected. The expression for horizontal translation is (x-h), so we end up with (x-(-2)), or (x+2).

Now that we have made the appropriate translations for the graph of "h", we can put it all together:

h(x)= (x+2)²-7(x+2)-6

Just one more step left! g(x) is 115% of h(x). In other words, the values of g(x) are 1.15 times those of h(x).

Thus, g(x)= 1.15((x+2)² - 7(x+2) - 6)

This equation shows us all of the translations and transformations to our graph, but it's a little cluttered. If you would like to present your equation in a simplified form, read on.

First, we simplify h(x).

h(x)= (x+2)(x+2) - 7x - 14 - 6

h(x)= x²+4x+4 - 7x - 14 - 6

h(x)= x² - 3x -16

Yielding g(x)= 1.15(x² - 3x -16)

Simplifying that equation gives us:

g(x)= 1.15x² - 3.45x - 18.4

Both of these equations are perfectly correct. The second one is just a simplified version. The advantage of the first equation, though, is that it tells us exactly what changes were applied to the initial function to get us the rule for "g."

Hope that helps!