write a quadratic function with zeros 1 and 9. write your answer using the variable x and in standard form…

write a quadratic function with zeros 1 and 9. write your answer using the variable x and in standard form with a leading coefficient of 1. f(x) =

write a quadratic function with zeros 1 and 9. write your answer using the variable x and in standard form with a leading coefficient of 1. f(x) =

Answer

Explanation:

Step1: Use zero - factor form

If (x = a) and (x = b) are the zeros of a quadratic function, then the function can be written in factored form as (f(x)=k(x - a)(x - b)). Here (a = 1), (b = 9) and (k = 1), so (f(x)=(x - 1)(x - 9)).

Step2: Expand the product

Use the FOIL method: ((x - 1)(x - 9)=x\times x+x\times(-9)+(-1)\times x+(-1)\times(-9)). [ \begin{align*} &=x^{2}-9x - x + 9\ &=x^{2}-10x + 9 \end{align*} ]

Answer:

(x^{2}-10x + 9)