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Lesson 5.4 Math Lab: Assess Your Understanding, pages 388–390
Use a graphing calculator.
1. a) Graph each system of equations. On the grids below:
• Sketch the graphs.
• Label them with their equations.
• Write the coordinates of the
points of intersection.
i) y = -2x2 + 8
3x - y = -3
y
3x y 3
(1, 6)
4
x
0
( 2.5, 4.5)
1
4
y 2x 2 8
ii) y = (x - 2)2 + 4
2x + y = 7
y (x 2)2 4
y
6
(1, 5)
4
2x y 7
2
x
0
iii) y = -1.5x2 + 6
x - 3y = - 21
2
10
y
8
No points of intersection
x 3y 21
y 1.5x 2 6
2
x
0
1
b) Use the graphs in part a to identify the different numbers of
solutions that a linear-quadratic system may have.
A linear-quadratic system may have 2 solutions, 1 solution, or no
solution.
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2. a) Graph each system of equations. On the grids below:
• Sketch the graphs.
• Label them with their equations.
• Write the coordinates of the points of intersection.
i) y = x2 + 5
y = -x2 + 7
y x2 5
y
8
(1, 6)
(1, 6)
4
2
x
2
2
0
y x 2 7
ii) y = (x - 3)2
y = -3x2 + 6x - 9
y (x 3)2
y
4
No points of intersection
x
0
2
4
4
8
y 3x 2 6x 9
iii) y = x2
y = -(x - 2)2 + 2
6
y
4
y x2
2
(1, 1)
2
0
x
2
2
y (x 2)2 2
iv) y = -2(x + 3)2 - 4
y = - 2x2 - 12x - 22
Infinite points of intersection
y
4
2
0
x
4
8
y 2(x 3)2 4
y 2x 2 12x 22
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5.4 Math Lab: Solving Systems of Equations Graphically—Solutions
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b) Use the graphs in part a to identify the different numbers of
solutions that a quadratic-quadratic system may have.
A quadratic-quadratic system may have infinite solutions, 2 solutions,
1 solution, or no solution.
3. Graph each system of equations, then write the coordinates of the
points of intersection to the nearest tenth.
a) y = 2x2 + 5x - 3
y = -3x + 2
b) y = - 2x2 + 2x + 5
y = x2 - 7x + 9
(0.5, 5.5) and (2.5, ⴚ2.2)
(ⴚ4.5, 15.6) and (0.5, 0.4)
4. Write the system of equations represented by each graph, then solve
the system. Give the solutions to the nearest tenth.
a)
b)
y
y
2
x
4
0
x
0
2
4
The line has slope 2 and
y-intercept 3: y ⴝ 2x ⴙ 3 ➀
The parabola has vertex
(2, 1) and is congruent to
➁
y ⴝ x2: y ⴝ (x ⴚ 2)2 ⴙ 1
Equations ➀ and ➁ form
the system.
The approximate solutions are:
(0.4, 3.7), (5.6, 14.3)
2
4
The line has slope ⴚ3 and
y-intercept 2: y ⴝ ⴚ3x ⴙ 2 ➀
The parabola has vertex
(2, 1) and is congruent to
y ⴝ ⴚ0.5x2: y ⴝ ⴚ0.5(x ⴚ 2)2 ⴙ 1
Equations ➀ and ➁ form
the system.
The approximate solutions
are: (0.6, 0.1), (9.4, ⴚ26.1)
➁
5. Explain the meaning of the points of intersection of a linear-
quadratic system or a quadratic-quadratic system.
The points of intersection of a linear-quadratic system or quadraticquadratic system are the points where the graphs of the equations in the
system intersect.The coordinates of each point of intersection satisfy both
equations in the system.
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5.4 Math Lab: Solving Systems of Equations Graphically—Solutions
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