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 = 2 , axis of symmetry x = 2 , 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 = 2 , axis of symmetry x = 2 , k < 0
Solution Summary: The author explains that the graph in option c matches with the given quadratic function, based on the conditions.
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.
The Mauna Loa Observatory in Hawaii records the carbon dioxide concentration y (in parts per million) in Earth’s atmosphere. The January readings for various years are shown in Figure . In the July 1990 issue of Scientific American, these data were used to predict the carbon dioxide level in Earth’s atmosphere in the year 2035, using the quadratic model y = 0.018t2 + 0.70t + 316.2 (Quadratic model for 1960–1990 data) where t = 0 represents 1960, as shown in Figure a. The data shown in figure b represent the years 1980 through 2014 and can be modeled by y = 0.014t2 + 0.66t + 320.3 (Quadratic model for 1980–2014) data where t = 0 represents 1960. What was the prediction given in the Scientific American article in 1990? Given the second model for 1980 through 2014, does this prediction for the year 2035 seem accurate?
Read and understand the lessons on transforming and graphing quadratic functions on pages 26– 30 in PIVOT 4A Grade - 9 Mathematics
Answer the following:
I. Transform the quadratic function defined by y = ax2 + bx+ c into the form y = a(x-h)² + k.
-1
--i-1
1. y = x2 – 6x – 3
2. y = 5x2 – 20x – 5
In Exercises 47–50, determine the x-intercepts of the graph of
each quadratic function. Then match the function with its graph,
labeled (a)-(d). Each graph is shown in a [-10, 10, 1]
by [-10, 10, 1] viewing rectangle.
47. у 3D х2 -бх + 8
48. y = x? – 2r – 8
49. y = x² + 6x + 8
50. y = x² + 2x – 8
а.
b.
C.
d.
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