Lesson 2

Lesson 2 Summary

 

© Amy Walters/851003/Fotolia

 

In this lesson you investigated the following questions:

• How can you sketch a graph of a quadratic function knowing the a-, p-, and q-values?
  
  
• How can you write an equation for a quadratic function from its graph?

You found that the quadratic function can provide information about the vertex:

p is the x-coordinate of the vertex. q is the y-coordinate of the vertex. The vertex coordinate = (p, q).

You also developed a rule to identify the number of x-intercepts. Your rule was similar to this:

 

If q = 0, only one x-intercept is present. If q ≠ 0, a and q are the same sign and there are no x-intercepts a and q are different signs and there are two x-intercepts

 

You used this information to graph a function and write an equation to represent a graph.

 

If you required the value of a, you could substitute the values of another point on the parabola into the function containing the known p- and q-values. You could then calculate the value of a as the unknown. It is convenient to choose the y-intercept as that other point because x = 0 for the y-intercept. Therefore, solving for a becomes simpler.

 

In the next lesson you will investigate how to solve quadratic equations in vertex form by completing the square. This skill will be a very powerful tool for you. You will also be introduced to another form of the quadratic function, and you will learn to convert back and forth between the two forms. This will enable you to model real-world situations even more effectively.