Lesson 5

Lesson 5 Summary

 

In this lesson you saw that quadratic functions can be written in a third way known as the factored form, y = a(x − r)(x − s). So, you have now seen that quadratic functions can be written in three forms:

• standard form, y = ax2 + bc + c
• vertex form, y = a(x − h)2 + k
• factored form, y = a(x − r)(x − s)

Each form of the function allows you to easily find different characteristics of a quadratic graph. The factored form of a quadratic function, which can also be written as f(x) = a(x − r)(x − s), allows you to quickly find the x-intercepts of the function because x = r and x = s. The axis of symmetry of the parabola can be found using the equation . The y-intercept can be calculated using the equation y = ars.

 

Quadratic functions can have zero, one, or two x-intercepts. By looking at the factored form of a quadratic function, the number of x-intercepts can be determined. If r and s are different values, there are two x-intercepts. If r and s are equal, there is only one x-intercept and the vertex is on the x-axis.

 

The zeros of a quadratic function correspond to the x-intercepts of the parabola that is defined by the function. Quadratic functions that do not have any zeros cannot be written in factored form.

 

You learned to apply these ideas to find answers to problems involving the trajectories of different projectiles.

 

In Lesson 6 you will investigate how to find the x-intercepts or roots of quadratic functions by factoring.