Lesson 5

Discover

 

The intercepts of a quadratic function usually provide information that is useful in solving a problem. The factored form allows you to identify the x- and y-intercepts of the quadratic function.

 

By now, you will recognize that a quadratic function in standard form, y = ax2 + bx + c, is made up of a trinomial, ax2 + bx + c. It follows, then, that you can factor a quadratic function using the same methods as you would use to factor a trinomial. The factored form of a quadratic function is written as y = a(x − r)(x − s).

 

In an earlier lesson you learned that the y-intercept is equal to the value of c in the standard form of a quadratic function. What if the function is in factored form? How can the y-intercept be found?

 

Substitute 0 for x in the factored form of the function and solve for y.

 

 

Recall that when you multiply two negative numbers together, you get a positive number. This means that y = a(−r)(−s) can also be written as y = a(r)(s). So, the y-intercept can be calculated from the factored form of a quadratic function using the formula y = ars.