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. Write your answer in expanded form "ax^2 + bx + c", where a,b,c are replaced by appropriate numbers.
+526 Let the quadratic eq. be ax2 + bx + c
∵ It has zeroes at x = 2 and x = -4
⇒ 4a + 2b + c = 0 ...(1)
16a - 4b + c = 0 ...(2)
and 9a + 3b + c = 6 ...(3)
Solving eq (1) and (2)
4a + 2b = 16a - 4b
12a = 6b ⇒ b = 2a
⇒ 4a + 4a + c = 0 ⇒ c = -8a
Solving eq (2) and (3)
16a - 4b = 9a + 3b - 6
7a = 7b - 6 ⇒7a = 14a - 6
⇒\(a= {6\over7}\)
\(b={12\over 7}\)
\(c={-48\over 7}\)
The equation is \({6\over 7}x^2+{12\over 7}x-{48\over 7}=0\)
