LESSON 6– USING THE QUADRATIC FORMULA – WORD PROBLEMS
RECALL:
THE QUADRATIC FORMULA
The solutions to the quadratic equation 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 are:
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
CONSECUTIVE NUMBERS such as 1, 2, 3,… or 15, 16, 17,…
How could we represent two consecutive numbers? → by 𝒙 and ______
How could we represent two even consecutive numbers? → by 𝒙 and _____
How could we represent two odd consecutive numbers? → by 𝒙 and ______
Area of a Triangle: 𝐴 =
𝑏ℎ
2
Area of a Cylinder: 𝐴 = 𝜋𝑟 2 ℎ
Example  The product of two consecutive even numbers is 5624. What are the numbers?
Example  One leg of a right triangle is 1 cm longer than the other leg. The length of the
hypotenuse is 9 cm greater than that of the shorter leg. Find the lengths of the
three sides.
Example  A rectangular park measures 100m by 60m. A path of constant width is to be
paved around the perimeter. The mayor wants to be sure that the path only
reduces the area of the park by 10%. What is the width of the path, rounded to
the nearest tenth of a meter?