A tank cannot have a negative width, so only the positive square root
makes sense. The tank will have a width of about 8.4 ft.@ 0 Got It? 3. a. Suppose the tank in Problem 3 will have a height of 4 ft and a volume of
500 ft3. What is the width of the tank to the nearest tenth of a foot?
b. Reasoning What are the disadvantages of using a graph to approximate
the solution to Problem 3? Explain.How can you w rite
the length o f the
tank?
The le n g th i is tw ic e th e
width w, so w rite the
length as 2 w.
You can solve some quadratic equations that model real-world problems by finding
square roots. In many cases, the negative square root may not be a reasonable solution.Ch o o si n g a Re a so n a b l e So l u t i o n 6RIDDED RESPONSE
Aquarium An aquarium is
designing a new exhibit to
showcase tropical fish. The
exhibit will include a tank
that is a rectangular prism
with a length € that is twice
the width w. The volume of^
the tank is 420 ft3. What is
the width of the tank to the
nearest tenth of a foot?V= Iwh Use th e fo rm u la fo r volum e o f a rectangular prism.
420 = (2w)w{3) Substitute 420 for V, 2 w fo r €, and 3 fo r h.
420 = 6w2 Simplify.
70 = w2 Divide each side by 6.
± V70 = w
± 8.366600265 « wFind the square roots o f each side.
Use a c a lc u la to r.Lesso n Ch eck
Do yo u k n o w H OW?
Solve each equation by graphing the related function or
by finding square roots.
- x2- 25 = 0
- 2x2 -8 = 0
- t2^144
- y2 - 225 = 0
MATHEMATICAL
Do y o u UN DERSTAND? PRACTICES- Vocabulary What are the zeros of a function? Give an
example of a quadratic function and its zeros. - C o m p a r e a n d C o n t r a s t When is it easier to solve
a quadratic equation of the form ax2 + c = 0 using
square roots than to solve it using a graph? - Reasoning Consider the equation ax2 + c = 0,
where a + 0. What is true of a and c if the equation
has two solutions? Only one solution? No solutions?
c
PowerAlgebra.com | Lesso n 9-3 So l v i n g Q u a d r a t i c Eq u a t i o n s 563