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

Apr 30, 2017

$y = {x}^{2} - 7 x + 3$

#### Explanation:

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

$a {x}^{2} + b x + c = y$
$a \cdot {2}^{2} + b \cdot 2 + c = - 7 R i g h t a r r o w c = - 7 - 4 a - 2 b$
$a {\left(- 2\right)}^{2} + b \left(- 2\right) + c = 21$
$a \cdot {1}^{2} + b \cdot 1 + c = - 3$

Substituting $c$ in the second
$4 a - 2 b - 7 - 4 a - 2 b = 21$
$- 4 b = 28 R i g h t a r r o w b = - 7$

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

Substituting $b$ and $c$ in the third
$a - 7 + 7 - 4 a = - 3$
$- 3 a = - 3 R i g h t a r r o w a = 1$