MATH HIGH SCHOOL
QUADRATIC EQUATIONS
EXERCISES
High School: Quadratic Equations
LESSON 2: SQUARE ROOT METHOD
EXERCISES
EXERCISES
1.
Estimate the roots of the graphs, if any roots exist.
y
20
15
10
5
5
10
15
20
25
x
Roots are at x = ______ .
A 5.5 and 25.5
B 4.5 and 24.5
C 14.5 and 21
D no real roots
2. Estimate the roots of the graphs, if any roots exist.
y
Roots are at x = ______ .
–10
x
–5
A –3 and –8
B –5 and –10
–5
C –5
D no real roots
–10
Copyright © 2015 Pearson Education, Inc.
7
High School: Quadratic Equations
LESSON 2: SQUARE ROOT METHOD
3.
EXERCISES
Estimate the roots of the graphs, if any roots exist.
y
Roots are at x = ______ .
A –4 and 0
10
B –5 and 1
C 4
5
–5
D no real roots
x
5
4. Find the roots of the equations. If real roots do not exist, explain how you know.
y = 12 −
5.
3 2
x
16
Find the roots of the equations. If real roots do not exist, explain how you know.
y = 5( x + 7)
2
6. Find the roots of the equations. If real roots do not exist, explain how you know.
y = 6 x 2 − 42
7.
Find the roots of the equations. If real roots do not exist, explain how you know.
y=−
1
( x − 1)2 − 18
2
8. Find the roots of the equations. If real roots do not exist, explain how you know.
y = −3 ( x − 4 ) + 9
2
Challenge Problem
9.
Copyright © 2015 Pearson Education, Inc.
Explain, with respect to the parameters a, h, and k, how an equation in the form
a(x – h)2 + k = 0 could have no real solutions.
8
MATH HIGH SCHOOL
QUADRATIC EQUATIONS
ANSWERS
FOR EXERCISES
High School: Quadratic Equations
LESSON 2: SQUARE ROOT METHOD
ANSWERS
ANSWERS
A.REI.4.b 1.
B
4.5 and 24.5
A.REI.4.b 2.
C
–5
A.REI.4.b 3.
D
no real roots
A.REI.4.b 4.
x = ±8
A.REI.4.b 5.
x = −7
A.REI.4.b 6.
x=± 7
A.REI.4.b 7.
No real roots. Algebraically, this is because you cannot take the square root of a
negative number and get a real number answer. Graphically, a quadratic function has
no real roots if it does not intercept the x-axis.
A.REI.4.b 8.
x =4± 3
Challenge Problem
A.SSE.2 9.
A.REI.1
A.REI.4.b
There are two situations for which the equation a ( x − h ) + k = 0 could have no real
solutions.
2
•
•
Copyright © 2015 Pearson Education, Inc.
The vertex of the function has a positive y-value, and the graph faces up.
This means a > 0 and k > 0 .
The vertex of the function has a negative y-value, and the graph faces down.
This means a < 0 and k < 0 . The parameter h affects the location of the
graph along the x-axis. It has no effect on the number of solutions.
43