Question

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

A. y = - (x + 1)^2 + 3
B. y = - (x - 1)^2 + 3
C. y = (x + 1)^2 + 3
D. y = (x - 1)^2 - 3

Answer 1

This answer is A.
Basically, the parabola opens downward so you know that the equation has a negative in the front...

Answer 2

Thus, (a) is correct.

`y=-(x+1)^2+3` is the equation of the given graph

Explanation:

Given a graph with vertex (-1 , 3)

We have to determine the equation of the graph and choose from the given options.

Since, the graph represents a quadratic equation.

The general form of representing a quadratic equation is
`y=a(x-h)^2+k` , where (h,k) is the vertex. a determine whether the graph open ups or down if it is positive then it open upward and vice versa.

For the given graph, vertex (-1 , 3)

Substitute h = -1 and k = 3 in
`y=a(x-h)^2+k` we get,

`y=a(x+1)^2+3`

Also the graph opens down ward so a has to be negative,

So
`y=-(x+1)^2+3`

Thus, Option (a) is correct.