We know that a polynomial of degree n with roots (x-intercepts) {x₁, x₂, ..., xₙ} and a leading coefficient A can be written as:
p(x) = A×(x - x₁)×...×(x - x₂)
Here we will find:
P(x) = (x - 1/2)×(x - 5)
Let's see how we found that:
Here we know that is a parabola, so n = 2, and the x-intercepts are:
x₁ = 1/2
x₂ = 5
And we do not know the leading coefficient, so we can assume A = 1.
Then the polynomial is just:
P(x) = (x - 1/2)×(x - 5)
The graph of this polynomial can be seen below.
If you want to learn more, you can read:
https://brainly.com/question/24371640
