Question

Without any programs, form a polynomial function of degree 2 with zero points x = 1 and x = 3 and whose graph passes through the point (5, 4).

BALIIIISS AND BALIIS

Answer 1

`y= \frac12 x^2 -2x +\frac32`

Explanation:

From the two zeroes, you can tell that the polynomial factors as
`y= A(x-1)(x-3)`. You have still one degree of freedom (determining how wide the parabola is. You can determine it with the other condition:

`4 = A(5-1)(5-3) \rightarrow 4= A(4)(2) \rightarrow A= \frac12`

Your function is
`y= \frac12 (x-1)(x-3) = \frac12 x^2 -2x +\frac32`