9-7 Linear, Quadratic, and Exponential M odels
Quick Review
Graphing data points or analyzing data numerically can
help you find the best model. Linear data have a common
first difference. Exponential data have a common ratio.
Quadratic data have a common second difference.Ex a m p l e
Graph the points (1 ,4 ), (4, 2), (2 ,3 ), (5 ,3 .5 ), and (6 ,5 ).
Which model is most appropriate?y
i\
1
X
0 LA quadratic model is
most appropriate.Ex e r c i s e s
Graph each set of points. Which model is most
appropriate for each data set?- (-3,0), (1,4), (-1,6), (2,0)
- (0, 6), (5, 2), (1, 4), (8, 1.5), (2, 3)
Write an equation to model the data.
49.
on50.
an
-1 2.5
0 5
110
220
3409-8 System s of Linear and Quad rat ic Equations
Quick Review
Systems of linear and quadratic equations can have two
solutions, one solution, or no solution. These systems can
be solved graphically or algebraically.Ex a m p l e
What are the solutions y — x2 — 7x — 40
of the system? y = - 3x + 37
y = x2 — 7x — 40 Use elimination.- (y = -3 x + 37) Subtract the equations.
0 = x2 - 4x - 77
0 = (x - 1 l)(x + 7) Factor.
jc—11 = 0 or x + 7 = 0 Zero-Product Property
x = 11 or x = -7 Solve for x.
Find the corresponding y-values.
y=-3(11)+ 37 = 4 y = —3(—7) + 37 = 58
The solutions are (11,4) and (-7 , 58).Ex e r c i se s
Solve each system by graphing.- y = x2 — 4x + 3 52. y = x2-2 x -l
y = — 3x + 5 y = —x — 1 - y = —2x2 + x + 2 54. y = x2 + x - 6
y = x y = 2x
Solve each system algebraically.- y = x2 + 2x - 45 56. y = x2 — 12x + 33
y = 6x + 51 - y = x2 + 19x + 39
y - 11 = 8x - y = x2 + 3x + 15
y + 45 = 19x
y = 4x - 30- y = x2 + 5x - 40
y + 1 = -5x - y = x2 + llx + 51
y = — lOx — 57 - W riting Explain howyou can use graphing to
determine the number of solutions of a system of
linear and quadratic equations.
606 Ch ap t er 9 Ch ap t er Revi ew