What is the equation of the graph below?

Question

The graph shows a parabola opening down with a vertex at negative 1 comma negative 4

Choose one answer.

A. y = -1(x - 4)2 + 1
 

B. y = -1(x + 1)2 + 4
 

C. y = 1(x + 1)2 - 4
 

D. y = 1(x + 4)2 - 1

Answer 1

If the parabola is opening down, similar to a n shape as opposed to a u shape, then none of these are the correct answer.

 

If it looks like a u, then C is the correct answer.

 

You need (x+1) inside the parenthesis because the graph is shifted to the left 1 (Left is +, right is -).

 

You need -4 at the end because the graph is shifted down four. (Down is -, up is +).

 

If it opens down like an n, then you need a -1 in front of the parenthesis to flip all of the positive y values into negative y values.

 

B would be correct if it were written -1((x+1)²+4) as the negative would distribute through.

 

Checking that, as written, B is incorrect:

Let x=-1

 

y=-1(-1+1)² + 4 = -1(0)+4 = 4

 

Your vertex is (-1,-4), so this is not correct.

 

Using different points, you can similarly check that C is incorrect if it looks like an n, not a u.

Answer 2

The answer is c