Question

How do you write the quadratic function in standard form given points `(-4,-7)`, `(-3,3)`, `(3, -21)`?

Answer 1

`y = -2x^2 -4x + 9`

Explanation:

`y = ax^2 + bx + c`

`(-4, -7):`
`-7= a(-4)^2 + b(-4) + c`
`16a - 4b + c = -7 => eq_1`

`(-3,3):`
`3 = a(-3)^2 + b(-3) + c`
`9a - 3b + c = 3 => eq_2`

`(3,-21):`
`-21 = a(3)^2 + b(3) + c`
`9a + 3b + c = -21 => eq_3`

`eq_(1,2&3)`
`16a - 4b + c = -7`
`9a - 3b + c = 3`
`9a + 3b + c = -21`
`=> a = -2, b = -4, c = 9`

`y = -2xxx^2 + -4xxx +9`
`y = -2x^2 -4x + 9`

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