# How do you write a quadratic function in intercept form who has x intercepts =16/3, -5/2 and passes through points (-9/2, -25/18)?

Jul 30, 2017

$y = - \frac{25}{354} \left(x - \frac{16}{3}\right) \left(x + \frac{5}{2}\right)$

#### Explanation:

$\text{since the roots are "x=16/3" and } x = - \frac{5}{2}$

$\Rightarrow \left(x - \frac{16}{3}\right) \text{ and "(x+5/2)" are factors}$

$\Rightarrow y = a \left(x - \frac{16}{3}\right) \left(x + \frac{5}{2}\right) \leftarrow \textcolor{red}{\text{ is the function}}$

$\text{to find a substitute "(-9/2,-25/18)" into the function}$

$\Rightarrow a \left(- \frac{9}{2} - \frac{16}{3}\right) \left(- \frac{9}{2} + \frac{5}{2}\right) = - \frac{25}{18}$

$\Rightarrow a \left(- \frac{59}{6}\right) \left(- 2\right) = - \frac{25}{18}$

$\Rightarrow \frac{59}{3} a = - \frac{25}{18}$

$\Rightarrow a = - \frac{25}{18} \times \frac{3}{59} = - \frac{25}{354}$

$\Rightarrow y = - \frac{25}{354} \left(x - \frac{16}{3}\right) \left(x + \frac{5}{2}\right)$
graph{-25/354(x-16/3)(x+5/2) [-10, 10, -5, 5]}