F.4 Quadratic equation... hard

Given that y = f(x)，where f(x) is a quadratic function:

x = 0，y = 0

x = 2，y = 4

x = 4，y = 6

x = 6，y = 6

x = 8，y = 4

...........

Find the maximum value of y = f(x) and find f(x)．How to do it without using

graphical method??

Sol

Set y=f(x)

Choose (x = 0．y = 0)，(x = 2．y = 4)，(x = 4．y = 6) only

f(x)=a(x－0)(x－2)+b(x－0)+ 0

f(2)=b(2－0)+0=4

b= 2

f(x)=a(x－0)(x－2)+2(x－0)=ax(x－2)+2x

f(4)=a*4*2+8=6

8a=－2

a=－1/ 4

f(x)=－1/4x(x－2)+2x=－x^2/4+5x/ 2

f(6)=－36/4+(5/2)*6=－9+15=6 correct

f(8)=－64/4+40/2=4 correct

So f(x)=－x^2/4+5x/ 2

f(x)=－1/4(x^2－10x)

=－1/4(x^2－10x+25)+25/4

=－1/4(x－5)^2+25/4

maxinum=25/4

這裏可以幫到你
http://yayantw.test.hansawell.net/yahoo.com.hk/hk/auction/1118037410