For Exercises 71–78, given a quadratic function defined by f ( x ) = a ( x − h ) 2 + k ( a ≠ 0 ) , match the graph with the function based on the conditions given. a > 0 , h < 0 , k < 0
For Exercises 71–78, given a quadratic function defined by f ( x ) = a ( x − h ) 2 + k ( a ≠ 0 ) , match the graph with the function based on the conditions given. a > 0 , h < 0 , k < 0
Solution Summary: The author explains that the graph in option d matches with the given conditions for the quadratic function.
For Exercises 71–78, given a quadratic function defined by
f
(
x
)
=
a
(
x
−
h
)
2
+
k
(
a
≠
0
)
, match the graph with the function based on the conditions given.
Find a quadratic function f (x) = ax2 + bx + c which has a vertex at (1, 1) and passes through (3, −3).
The following table shows the average new car transaction price in the USA as a percentage of disposable income.
Year(s)
% of Disposable Income
1960
0
43
1975
15
77
1983
23
85
(A) Find a quadratic function f(x) = ax2 + bx + c that fits the data, where x represents the number of years after 1960.
Consider f(x)=ax3+bx2+cx+d
Under what conditions on a,b,c,and d does the graph of a cubic function even have turning points?
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