Download Warm Up

Warm Up
 1.) Graph the set of points (-2, 7), (-1, 4), (0, 1), and
(1, -2). Which model is most appropriate for the set?
(linear or exponential)
 2.) Which kind of function best models the data? Use
differences or ratios.
x
y
0
0
1
-0.5
2
-2
3
-4.5
4
-8
9.8 Systems of Linear and
Quadratic Equations
Objective
 Solve systems of linear and quadratic equations.
Systems of Equations
 You can solve systems of linear and quadratic
equations graphically and algebraically. There can be
two solutions, one solution, or no solution.
Example 1 – Solving By Graphing
 What are the solutions of the system? Solve by
graphing.
 y = x2 + x + 2
 y=x+6
Example 2 – Using Elimination
 The equations y = 24x + 15 and y = -x2 + 120x + 15
model the daily sales of two types of computers,
where x is the number of days since the computers
were put on sale. One what day was the same
number of each computer sold.
Extra Example 2
 Since opening day, attendance at Pool A has
increased steadily, while at Pool B first rose and then
fell. The equation for attendance at Pool A is
modeled by y = 32x + 74. The equation for Pool B’s
attendance is y = -x2 + 39x + 64. On what day(s) was
the attendance the same at both pools.
Example 3 – Using Substitution
 What are the solutions of the system?
 y = x2 – 4x + 2
 y = -x
Extra Example 3
 What are the solutions of the system?
 y = 12x + 30
 y = x2 + 11x - 12
Assignment
 Pg. 585 (9 – 11 all, 14 – 20 all)
Bellwork Quiz
 1.) What are the solutions of x2 + 12x + 32 = 0? Use
the quadratic formula.
 2.) What is the number of solutions of
4x2 + 12x + 9 = 0?
 3.) Graph the set of points (-2, 7), (-1, 4), (0, 1), and
(1, -2). Which model is most appropriate for the set?
(linear or exponential)
Warm Up
 1.) Use elimination to solve the system:
 y = x2 – 13x + 52 and y = -14x + 94
 2.) Use substitution to solve the system:
 y = x2 – 6x + 9 and y = -x + 5
Assignment
 Pg. 590 – 592 (5, 6, 10, 17 – 20 all, 23 – 26 all, 30 –
33 all, 38 – 43 all, 47 – 50 all, 54 – 58 all)
Warm Up
 Solve each equation by completing the square.
 1.) x2 + 8x = 180
 2.) t2 – 4t – 165 = 0
Warm Up
 Use the quadratic formula to find the solutions.
 1.) -3x2 – 11x + 4 = 0
 2.) 7x2 – 2x = 8
Bellwork Quiz
 1.) Use algebra to solve the system:
 y = x2 – 6x + 9 and y = -x + 5
 2.) Solve the equation by completing the square:
 x2 + 8x = 180
 3.) Use the quadratic formula to solve:
 -3x2 – 11x + 4 = 0