Question

What is the equation of the graph below?

y = − (x − 3)2 + 1
y = − (x + 1)2 + 4
y = (x + 1)2 − 4
y = (x − 4)2 + 1

Answer 1

The first option would be the answer

Answer 2

The answer to your question is the first option y = -(x - 3)² + 1

Explanation:

From the graph, we know that it is a vertical parabola with Vertex (3, 1) that opens downwards.

Equation (x - h)² = -4p(y - k)

Also from the graph we know that the parabola passes by (2, 0)

- Find p

(2 - 3)² = -4p(0 - 1)

-Simplification

(-1)² = -4p(-1)

1 = 4p

-Result

p = 1/4

- Equation of the parabola

(x - 3)² = -4(1/4)(y - 1)

-Simplification

-(x - 3)² = y - 1

-Solve for y

y = -(x - 3)² + 1