Question

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

Answer 1

`y = x² -5x + 6`

Explanation:

The general form of this type of quadratic is:

`y = k(x - r_1)(x - r_2)`

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(4 - 2)(4 - 3)`

`2 = k(2)(1)`

`k = 1`

The equation is:

`y = (x - 2)(x - 3)`

`y = x² -5x + 6`