Question

Which polynomial could have the following graph?

y = (x + 3)(x - 1)(x - 5)
y = (x - 3)(x + 1)(x + 5)
y = -(x + 3)(x - 1)(x - 5)
y = -(x - 3)(x + 1)(x + 5)

Answer 1

The graph shows the solutions:

x1 = -3 ⇒ x + 3 = 0

x2 = 1 ⇒ x - 1 = 0

x3 = 5 ⇒ x - 5 = 0

The polynomial follows: y = (x + 3)(x - 1)(x - 5)

.

Answer 2

y= (x+3) (x-1) (x-5)

Explanation:

The graph crosses the x axis at the points -3,1,5

These are also called the zeros

f(x) =k (x-a) (x-b) (x-c) .....

where a,b,c,... are the zeros of the function and k is a constant

f(x) = k * (x--3) (x-1) (x-5)

f(x) = k(x+3) (x-1) (x-5)

To help determine the value of k

Take another point at x = 0, we know the value is positive

f(0) = k(3) (-1) (-5)

f(0) = k(15)

That means k must be greater than 0 Looking at the graph, it should be around 1

f(x) = (x+3) (x-1) (x-5)