Changing Parabolic Equations from
Standard Form to Vertex Form
If we have any polynomial in the form x2 + bx
how can we convert it to a perfect square polynomial?
3.3
Example 1: Your Turn
Rewrite each function in vertex form by
completing the square.
Answer
a) y = x2 + 8x – 7
b) y = 2x2 – 20x
c) y = –3x2 – 18x – 24
a)
b)
c)
3.3
Example 2: Your Turn
Answer
a) Convert the function y = –3x2 – 27x + 13 to vertex form.
b) Verify that the two forms are equivalent.
3.3
Example 3: Your Turn
Consider the function y = 3x2 + 30x + 41.
a) Complete the square to determine the vertex of the graph of the
function.
b) Use
and the standard form of the quadratic function
Answer
to determine the vertex. Compare with your answer from part a).
A farmer with 750 m of fencing wants to enclose a rectangular area and
then divide it into four pens with 3 fences parallel to one side of the
rectangle. What is the largest possible total area of the four pens?
Find two positive numbers whose sum is 13
if the sum of their squares is a minimum.
Working Examples 1 - 3, pp. 134-136
& pp. 137 - 141, # 1 - 10