# How do you write a quadratic function in intercept form whose graph has x intercepts -3, -2 and passes through (-4, -6)?

##### 1 Answer
Jul 25, 2017

The quadratic equation in intercept form is $y = - 3 \left(x + 3\right) \left(x + 2\right)$.

#### Explanation:

The quadratic equation in intercept form is $y = a \left(x - p\right) \left(x - q\right)$

where $p = - 3 \mathmr{and} q = - 2$ are x -intercepts . So The quadratic

equation in intercept form is $y = a \left(x + 3\right) \left(x + 2\right)$. The parabola

passes through $\left(- 4 , - 6\right)$ , which will satisfy the equation of

parabola. $\therefore - 6 = a \left(- 4 + 3\right) \left(- 4 + 2\right) \mathmr{and} - 6 = 2 a$ or

$a = - 3$. Hence the quadratic equation in intercept form is

$y = - 3 \left(x + 3\right) \left(x + 2\right)$.

graph{-3(x+3)(x+2) [-10, 10, -5, 5]} [Ans]