Question

Determine the equation of the graph and select the correct answer below.

y = (x + 2)^2 + 4
y = (x − 2)^2 − 4
y = –(x − 2)^2 − 4
y = –(x + 2)^2 − 4

Answer 1

The vertex form of a square function:

`f(x)=a(x-h)^2+k`

(h, k) - coordinates of a vertex

We have the vertex (-2, -4) → h = -2 and k = -4

Answer:
`y=(x-(-2))^2-4=(x+2)^2-4`

Answer 2

Answer: y = -(x - 2)^2 - 4

Explanation:

If we have a function of the form:

y(x) = a*(x - b)^2 + c

The vertex of the function will be located at the point (b, c)

This happens because the square therm has a minimum (or maximum if a is negative) when x = b, so this is is the minimal value of x, and the minimal value of y is c.

Here in the graph, we can see that the vertex is at (-2, - 4) so we have that c = -4, and b = -2

the function is:

y(x) = a*(x + 2) - 4

And because the "hands" of the graph are coming down, we know that the value of a is negative, and the only option where a is negative, b = -2 and c = -4 is the third option:

y = -(x - 2)^2 - 4