Bài tập toán cơ bản số 40

Created by T. Madas
Question 41
Complete the square in the following quadratics and then state the coordinates of their maximum
or minimum point.
2

min ( −1, −1)

2

min ( 4, −16 )

a) y = x 2 + 2 x = ( x + 1) − 1
b) y = x 2 − 8 x = ( x − 4 ) − 16
2

min (1,6 )

c) y = x 2 − 2 x + 7 = ( x − 1) + 6
2

d) y = x 2 + 6 x + 10 = ( x + 3) + 1
2

e) y = x 2 − 12 x + 27 = ( x − 6 ) − 9

min ( −3,1)
min ( 6, −9 )

Question 42
Complete the square in the following quadratics and then state the coordinates of their maximum

or minimum point.

a) y = x 2 + 12 x + 36 = ( x + 6 )

2

min ( −6,0 )

2

b) y = x 2 − 4 x + 6 = ( x − 2 ) + 2
2

c) y = x 2 − 16 x + 40 = ( x − 8 ) − 24
2

d) y = x 2 − 8 x + 18 = ( x − 4 ) + 2
2

e) y = x 2 + 14 x + 50 = ( x + 7 ) + 1

min ( 2, 2 )
min ( 8, −24 )
min ( 4, 2 )
min ( −7,1)

Created by T. Madas


Created by T. Madas

Question 43
Complete the square in the following quadratics and then state the coordinates of their maximum
or minimum point.

− 94

min 72 , − 94

2

+ 31
4

min − 32 , 31
4

)

(

)

b) y = x 2 + 3x + 10 = x + 32

(

2

(

a) y = x 2 − 7 x + 10 = x − 72

c) y = x 2 + x + 1 = x + 12

)

2

(

(
(

min − 12 , 43

+ 43
2

d) y = 2 x 2 − 8 x + 10 = 2 ( x − 2 ) + 2
2

e) y = 3 x 2 − 18 x + 24 = 3 ( x − 3) − 3

)
)

)

min ( 2, 2 )
min ( 3, −3)

Question 44
Complete the square in the following quadratics and then state the coordinates of their maximum
or minimum point.
2

a) y = 4 x 2 − 8 x + 28 = 4 ( x − 1) + 24
2

min ( −2, −5)

2

min ( −4, −3)

b) y = 5 x 2 + 20 x + 15 = 5 ( x + 2 ) − 5
c) y = 3 x 2 + 24 x + 45 = 3 ( x + 4 ) − 3
2

d) y = 4 x 2 − 8 x + 16 = 4 ( x − 1) + 12
2

e) y = 5 x 2 + 10 x = 5 ( x + 1) − 5

min (1, 24 )

min (1,12 )
min ( −1, −5 )

Created by T. Madas