# How do you write a quadratic equation with x - intercepts: 2,3 point: (4,2)?

Oct 5, 2016

y = x² -5x + 6

#### Explanation:

The general form of this type of quadratic is:

$y = k \left(x - {r}_{1}\right) \left(x - {r}_{2}\right)$

where $k$ is a scaling factor that allows you to force the equation to pass through any given point and ${r}_{1}$ and ${r}_{2}$ are the x intercepts of the curve. Substituting the given information into the general form:

$2 = k \left(4 - 2\right) \left(4 - 3\right)$

$2 = k \left(2\right) \left(1\right)$

$k = 1$

The equation is:

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

y = x² -5x + 6