Page 130 - Math Course 2 (Book 1)

Perfect Square Trinomials

2x + 9 = 0 Set the repeated
factor equal to zero.

2x = –9 b = 7 ± 6 Add 7 to each side

9 b = 7 + 6 or b = 7 – 6 Separate into two
x = – Solve for x.
2 equations.
= 13 = 1 Simplify.

Real World Example The roots are 1 and 13. Check

Answer each solution in the original
PHYSICAL SCIENCE equation.
A book falls from a shelf that is 60
inches above the f oor. A model for
2
the height h in feet of an object dropped from an Solve (x + 9) = 8.
2
initial height of h0 feet is h = –16t + h , where t is 2
0
the time in seconds after the object is dropped. Use (x + 9) = 8 Original equation.
this model to determine approximately how long it 8
took for the book to reach the ground. x + 9 = ± Square Root Property
2
h = –16t + h Original equation x = –9 ± 2 2 Subtract 9 from each
0 side. = 2 2
8
2
0 = –16t + 5 Replace h with 0 and h0
{ – 9 ± 2 2 }
with 5. The solution set is
Using a calculator, the approxi-
–5 = –16t 2 Subtract 5 from each side. Answer mate solutions are –9 + 2 2
0.3125 = t 2 Divide each side by –16. or about –6.17 and –9 – 2 2
or about –11.83
±0.56 ≈ t Take the square root of
each side. Check
You can check your answer using a graphing
2
calculator. Graph y = (x + 9) and y = 8. Using the
INTERSECT feature of your graphing calculator, f nd
Since a negative number does not 2
make sense in this situation, the where (x + 9) = 8. The check of –6.17 as one of the
Answer solution is 0.56. This means that approximate solutions is shown.
it takes about 0.56 second for the
book to reach the ground. y

Use the Square Root Property to
Solve Equations

Examples

2
Solve (b – 7) = 36.
0
x
2
(b – 7) = 36 Original equation
b – 7 = ± 36 Square Root Property Intersection
b – 7 = ± 6 36 = 6 • 6 X = –6.171573 Y = 8

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