Page 777 - Algebra 1

Example
1
Solving by Graphing
Solve each system of equations by graphing. Then check the solution. a. y=x2
y=4
SOLUTION Graph the parabola y = x2 and the 16
horizontal line y = 4.
The line intersects the parabola at (2, 4) and (-2, 4). The solution of the system is the ordered pairs (2, 4) and (-2, 4).
(-2, 4)
Check
y = x2
4 (2)2 4=4 ✓
b. y=x2
y = -4x - 4
y = x2
4 (-2)2 4=4 ✓
Caution
Be sure to check all solutions in both of the original equations of the system.
SOLUTION Graph the parabola and the line. The line intersects the parabola at only one
point. The solution is (-2, 4). Check
y = x
y = x2
4 (-2)2 4=4 ✓
c. y=2x2-9 y = 4x - 9
y = -4x - 4
4 -4(-2) - 4 4=4 ✓
SOLUTION Thegraphsof y=2x2-9andy=4x-9 show two points of intersection. The coordinates of those two points are (2, -1) and (0, -9).
Check Verifythat(2,-1)isasolution.
y=2x2 -9
-1 2(2)2 -9
-1=-1 ✓
Verify that (0, -9) is a solution.
y=4x-9 -1 4(2)-9 -1=-1 ✓
y=2x2 -9 -9 2(0)2 -9 -9=-9 ✓
y=4x-9 -9 4(0)-9 -9=-9 ✓
y
y
=
x
2
762 Saxon Algebra 1
y=4
8
(2, 4)
x
-4
-2
2
4
-8
-16
16
y
2
8
(-2,
4)
x
-4
-2
2
4
-8
y = -4x -
4
-16
y
16
y =
2
2x -9
8
(2, -1)
x
-4
4
y = 4x -9
(0, -
9)