3.6 Quadratic Function, SPM Practice (Short Question)


Question 3:
The straight line y = 5x – 1 does not intersect with the curve y = 2x2 + x + h.
Find the range of values of h.

Solution:
y=5x1         …… (1) y=2 x 2 +x+h …… (2) Substitute (1) into (2), 5x1=2 x 2 +x+h 2 x 2 +x+h5x+1=0 2 x 2 4x+h+1=0                   b 2 4ac<0 ( 4 ) 2 4( 2 )( h+1 )<0              168h8<0                             8<8h                             h>1


Question 4:
Find the maximum value of the function 5 – x – 2x2 , and the corresponding value of x.

Solution:
5x2 x 2 =2 x 2 x+5 =2[ x 2 + 1 2 x 5 2 ] =2[ x 2 + 1 2 x+ ( 1 4 ) 2 ( 1 4 ) 2 5 2 ] =2[ ( x+ 1 4 ) 2 1 16 5 2 ] =2[ ( x+ 1 4 ) 2 41 16 ] =2 ( x+ 1 4 ) 2 +5 1 8


5x2 x 2  has a maximum value when 2 ( x+ 1 4 ) 2 =0               x= 1 4 The maximum value of 5x2 x 2  is 5 1 8 .

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