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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.

Jun 15, 2021

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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 $${6\over 7}x^2+{12\over 7}x-{48\over 7}=0$$

Jun 16, 2021