C Challenge
Write a quadratic equation with the given solutions.
-
3
+
5
2
,
3
−
5
2
fraction 3 plus square root of 5 , over 2 end fraction . comma . fraction 3 minus square root of 5 , over 2 end fraction
-
−
5
+
13
2
,
−
5
−
13
2
fraction negative 5 plus square root of 13 , over 2 end fraction . comma . fraction negative 5 minus square root of 13 , over 2 end fraction
-
−
5
+
17
4
,
−
5
−
17
4
fraction negative 5 plus square root of 17 , over 4 end fraction . comma . fraction negative 5 minus square root of 17 , over 4 end fraction
Solve each equation.
-
|
5
−
2
x
2
|
=
5
vertical line 5 minus , 2 x squared , vertical line equals 5
-
|
x
2
−
4
x
|
=
3
vertical line , x squared , minus 4 x vertical line equals 3
-
|
x
2
+
4
x
+
3
|
=
8
vertical line , x squared , plus 4 x plus 3 vertical line equals 8
- Use the Quadratic Formula to prove each statement.
- The sum of the solutions of the quadratic equation
a
x
2
+
b
x
+
c
=
0
eh , x squared , plus b x plus c equals 0 is
−
b
a
.
negative , b over eh , .
- The product of the solutions of the quadratic equation
a
x
2
+
b
x
+
c
=
0
eh , x squared , plus b x plus c equals 0 is
c
a
.
c over eh , .
- Explain the meaning of the value
b
2
−
4
a
c
2
a
fraction square root of b squared , minus 4 eh c end root , over 2 eh end fraction in terms of the graph of the standard quadratic function
y
=
a
x
2
+
b
x
+
c
.
y equals eh , x squared , plus b x plus c .
Standardized Test Prep
GRIDDED RESPONSE
SAT/ACT
- How many different real solutions are there for
2
x
2
−
3
x
+
5
=
0
?
2 x squared , minus 3 x plus 5 equals 0 question mark
- What is the y-value of the y-intercept of the quadratic function
y
=
2
(
x
+
2
)
2
−
5
?
y equals 2 open x plus 2 , close squared , minus 5 question mark
- What is the x-value in the solution to the system
{
3
x
+
y
=
−
7
2
x
−
2
y
=
−
10
?
left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus y equals negative 7 , row2 column 1 , 2 x minus 2 y equals negative 10 , end table . question mark
-
The graph of the system of inequalities
{
y
≤
1
2
x
+
3
y
≥
6
x
−
30
x
≥
0
y
≥
0
left brace . table with 4 rows and 1 column , row1 column 1 , y less than or equal to , 1 half , x plus 3 , row2 column 1 , y greater than or equal to 6 x minus 30 , row3 column 1 , x greater than or equal to 0 , row4 column 1 , y greater than or equal to 0 , end table is shown below.
What is the maximum value of the function
P
=
3
x
−
4
y
p equals 3 , x minus , 4 y for the (x, y) pairs in the bounded region shown?
Mixed Review
See Problem 4-6.
Solve each equation by completing the square.
-
x
2
−
8
x
−
20
=
0
x squared , minus 8 x minus 20 equals 0
-
2
y
2
=
4
y
−
1
2 y squared , equals 4 y minus 1
-
x
2
−
3
x
−
8
=
0
x squared , minus 3 x minus 8 equals 0
See Problem 1-3.
Simplify by combining like terms.
-
z
2
+
8
z
2
−
2
z
+
5
z
z squared , plus 8 , z squared , minus 2 z plus 5 z
-
4
k
−
x
−
3
k
+
5
x
4 k minus x minus 3 k plus 5 x
-
4
y
−
(
2
y
+
3
x
)
−
5
x
4 y minus open 2 y plus 3 x close minus 5 x
Get Ready! To prepare for Lesson 4-8, do Exercises 88–90.
See p. 973.
Simplify each expression.
-
(
−
2
)
2
+
8
2
square root of open , negative 2 , close squared . plus , 8 squared end root
-
3
2
+
4
2
square root of 3 squared , plus , 4 squared end root
-
5
2
+
(
−
12
)
2
square root of 5 squared , plus . open , negative 12 , close squared end root
