Question

How do you write a quadratic function in standard form whose graph passes through points (2,-7), (-2,21), (1,-3)?

Answer 1

`y = x^2 - 7 x + 3`

Explanation:

3 points, 3 equations, 3 variables {a, b, c}

`ax^2 + bx + c = y`
`a * 2^2 + b*2 + c = -7 Rightarrow c = -7 -4a -2b`
`a(-2)^2 + b(-2) + c = 21`
`a*1^2 + b*1 + c = -3`

Substituting `c` in the second
`4a - 2b -7 -4a - 2b = 21`
`-4b = 28 Rightarrow b = -7`

Substituting `b` in `c`
`c = -7 -4a + 14 = 7 - 4a`

Substituting `b` and `c` in the third
`a - 7 + 7 - 4a = -3`
`-3a = -3 Rightarrow a = 1`