Aim #57: How do we solve quadratic word problems?
Homework: Worksheet
Do Now: Solve for x:
4x
25
=
9
x
We learned how to solve a quadratic equation by factoring, completing the square, and
using the quadratic formula. Even though factoring is not always available to use to
solve a quadratic equation, it should be attempted first.
Find three consecutive odd integers such that the product of the two smaller exceeds
the largest by 52.
As we can see, mathematically there are 2 solutions to the equation above. Since the
word problem calls for the domain, x, to be an odd integer, one of our solutions is
rejected.
Solutions that are mathematically correct but are excluded from the domain
(rejected) are called _________________ solutions.
1) The length of one leg of a right triangle is 5. The lengths of the other leg and the
hypotenuse are consecutive integers. Find the length of the hypotenuse.
2) The sum of the squares of two positive consecutive odd integers is 130. What are
the integers?
3) Charlie wants to build a rectangular flower bed in his garden. He'd like the length
to be four less than twice the width and the area to be 70 sq ft. Determine the
dimensions of the rectangular flower bed.
4) In the figure below, the area of rectangle LAND is 154 sq in, and the side of
square S is x. Using the information in the figure below, what is the length of side x?
L
A
4
S
D
x
N
7
5) The length and width of a picture is 11 by 8. John wants to put a picture frame of
uniform width around the picture. The area of the picture with the picture frame is
180. Determine the width of the picture frame.
6) The height of a triangular metal plate is 6 times the measure of the base. The area
of the plate is 120 sq. in. In simplest radical form, what is the measure of the base?
Sum it up!
We can solve quadratic equations in multiple ways. However, we should always look
to see if the quadratic is factorable first before choosing the quadratic formula
or completing the square methods.
After solving, we must be able to identify if extraneous solutions need to be
rejected from the solution set due to the restrictions on the domain.