Question

A graph is shown below.

Which function represents the graph?

Answer 1

Given that the graph of a parabola.

We need to determine the function that represents the graph.

Function of the graph:

From the graph, it is obvious, that the x - intercepts of the graph are
`x = -3,x=-5`

Thus, the equation can be written as

`y=(x-(-3))(x-(-5))`

Simplifying the terms, we have;

`y=(x+3)(x+5)`

Multiplying, we get;

`y=x^2+5x+3x+15`

Adding the like terms, we have;

`y=x^2+8x+15`

Writing it as function, we have;

`f(x)=x^2+8x+15`

Hence, the function of the graph is
`f(x)=x^2+8x+15`