Give an example of a quadratic function that has zeroes at x=2 and x=4, and that takes the value 6 when x=3.
Enter your answer in the expanded form "ax^2 + bx + c", where a,b,c are replaced by appropriate numbers.
+128407 We can write this form, first
Since x = 2 and x = 4 are zeroes we know that it will factor as
y = a ( x - 2) (x - 4) so.....when x = 3 , y = 6 and we can solve for "a"
6 = a(3 - 2) ( 3 - 4)
6 = -1 a ⇒ a = -6
So.....the fumction is
y = -6 ( x - 2)(x - 4)
y = -6 (x^2 - 6x + 8)
y = -6x^2 +36x - 48
Here's a graph to confirm this :
https://www.desmos.com/calculator/q6hbimtgh1
