Learning Resources
Lesson
When the vertex and at least one other point of a parabola are given, the equation can be found either directly from the graph or algebraically using the transformational form of the quadratic function. Study these two methods given in the text book on pages 36 and 37.
Complete the Focus questions as assigned in the activities.
If you need to see another example that illustrates these methods go to the next page before beginning the activities.
Find the equation of a parabola with vertex (4, -6) and passes through the point (3, -4).
Solution
Method 1 : Starting with the equation 
The vertex (4, -6) represents a horizontal translation of 4 units right and a vertical translation of 6 units down These translations are represented as
Compare the patterns for the new function and . Since the second point is 1 unit to the left of the vertex and above it , we have the following:
-
over 1 up 1
-
New function over 1 up 2
Therefore, the vertical stretch is 
upward which means a is positive.
The quadratic function describing the parabola will be 
Method 2 : We know the transformational form of the equation is 
where (p, q) represents the vertex of the parabola. From the problem we have the vertex (4, -6) and following equation:
To find the value of k substitute the values for x and y from the second point (3, -4)
Substituting into the transformational form we have
Activity
Focus questions p.37-38. Complete 35, 36, 37 and 38
Think About p.37 ( 3 parts) and p.38
Check Your Understanding p.38 - 39. Complete 39 to 45 inclusive
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
Find the transformational form of the parabola with vertex (-2, -3) and passing through the point (4, -8)
Check your answer.