Question

What is the equation of the graph below?
S
2.
1
-
3
Oy = -(x - 3)2 + 1
Oy = -(x + 1)2 + 4
Oy = (x + 1)2 - 4
Oy = (x - 4)2 + 1

Answer 1

Answer:

$y=-(x-3)^2+1$

Step-by-step explanation:

Hi there!

Vertex form: $y=a(x-h)^2+k$ where $a$ is a scale factor and $(h,k)$ is the vertex of the parabola

On the graph, we can determine that the vertex of this parabola is (3,1). Plug this into $y=a(x-h)^2+k$:

$y=a(x-3)^2+1$

The value of a must either be -1 or 1 because the graph has not been stretched or compressed vertically. How can we tell? Well, starting from the vertex, if we increase x by 1, y only changes by 1. If we decrease x by 1 starting from the vertex, y only changes by 1. This wouldn't be the case if the graph had been stretched or compressed.

Now, because this is a downward-facing parabola, we know that the value of a is negative. Because a can only be -1 or 1, a is therefore -1. Plug this into $y=a(x-3)^2+1$:

$y=-(x-3)^2+1$

I hope this helps!