Bài tập toán cơ bản số 39

Created by T. Madas

COMPLETING
THE
SQUARE

Created by T. Madas


Created by T. Madas
Question 39
Complete the square in the following quadratics and then state the coordinates of their maximum
or minimum point.
2

a) y = x 2 − 8 x − 2 = ( x − 4 ) − 18
2

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

min ( 4, −18 )
min ( −3,1)
min ( 2, −3)

c) y = x 2 − 4 x + 1 = ( x − 2 ) − 3
2

d) y = x 2 + 4 x + 9 = ( x + 2 ) + 5
2

e) y = x 2 + 8 x + 20 = ( x + 4 ) + 4

min ( −2,5 )
min ( −4, 4 )

Question 40
Complete the square in the following quadratics and then state the coordinates of their maximum
or minimum point.
2

a) y = x 2 − 6 x + 10 = ( x − 3) + 1

min ( 3,1)

2

min ( 5, −1)

2

min ( −5,5)

b) y = x 2 − 10 x + 24 = ( x − 5 ) − 1
c) y = x 2 + 10 x + 30 = ( x + 5 ) + 5
2

d) y = x 2 − 12 x − 4 = ( x − 6 ) − 40
2

e) y = x 2 + 14 x + 29 = ( x + 7 ) − 20

min ( 6, −40 )
min ( −7, −20 )

Created by T. Madas