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

1 Answer
Oct 5, 2016

#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#