Question

Which function could be represented by the graph on the

coordinate plane?
f (x) = (x-8)2 + 6
f(x) = (x + 8)2 + 6
f(x) = (x + 8)2 – 6
f(x) = (x – 8)2 - 6

Answer 1

Answer: f(x) = (x - 8)^2 - 6

The equations are written in vertex form, so we can tell the point of the vertex from each equation.
Vertex form is y = a( x - h)^2 + k
Where (h,k) is the vertex

From looking at the graph, we know the vertex will have a positive x value, and a negative y value.
So h will be positive, and k will be negative.
f(x) = (x-8)^2 - 6 is the only answer choice with a positive h and a negative k.

I attached a photo to better show what vertex form is.

Answer 2

D

Explanation:

Start by the easier part. The graph is below the x axis. The only way that can happen is if f(x) = (x - b)^2 - 6

Now what you have done is eliminate answers a and b.

The much harder part is dealing with the 8. Is it plus or minus. It turns out that the reason this is more complex is that it is anti intuitive.

- 8 means move right.

+ 8 means move left - just exactly the opposite of what you have been taught about a number line.

Since the graph is moving right, then you use -8

The answer becomes

y = (x - 8)^2 - 6 which is D