​Zero Product Property

​When the product of two or more factors is zero, at least one of the factors must equal zero. That is, if a · b = 0, then either a = 0 or b = 0 (or both). This property is used to solve equations in factored form. For example, given the equation (x – 4)(x + 5) = 0, x – 4 = 0 or x + 5 = 0 (or both). You can see that x = 4 and x = –5 are solutions and that they are the only possible solutions because there are no other numbers that make either factor zero. The Zero Product Property can be used to solve factorable quadratic equations.

​Solve the following Quadratic Function:

​ a. y= 2x² +5x-12

Step 1: Factor (​2x-3)(x+4) Factor

​Step 2: Apply the Zero Product Property

2x-3=0 x+4=0

2x-3+3=0+3 x+4-4=0-4

2x=3​ x=-4

​ x=3/2

​ ​x-intercept: ( 3/2, 0)

( -4,0)

​

​

​Solve for y-intercept:

​ Let x=0

​​ y=2x²+5x-12

​ y= 2(0)² +5(0)-12

​

​ y= -12