College Algebra, 2013a

204 Linear and Quadratic Functions
5. f(x) =2x 2 −(
4x − 1=2(x − 1) 2 − 3
2−
x-intercepts
√ ) (
6
2+
2
, 0 and
√ )
6
2
, 0
y-intercept (0, −1)
Domain: (−∞, ∞)
Range: [−3, ∞)
Increasing on [1, ∞)
Decreasing on (−∞, 1]
Vertex (1, −3) is a minimum
Axis of symmetry x =1
y
4
3
2
1
−1 1 2 3
−1
−2
−3
x
6. f(x) =−3x 2 +4x − 7=−3 ( x − 2 2
3)
−
17
3
No x-intercepts
y-intercept (0, −7)
Domain: (−∞, ∞)
Range: ( −∞, − 17 ]
3
Increasing on ( −∞, 2 ]
3
Decreasing on [ 2
3 , ∞)
Vertex ( 2
3 , − 17 )
3 is a maximum
Axis of symmetry x = 2 3
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
−11
−12
−13
−14
y
1 2
x
7. f(x) =x 2 + x +1= ( x + 1 2
2)
+
3
4
No x-intercepts
y-intercept (0, 1)
Domain: (−∞, ∞)
Range: [ 3
4 , ∞)
Increasing on [ − 1 2 , ∞)
Decreasing on ( −∞, − 1 ]
2
Vertex ( − 1 2 , 3 4)
is a minimum
Axis of symmetry x = − 1 2
y
4
3
2
1
−2 −1 1
x