EXERCISES Find an equation for the family of linear functions with slope 2 and s

Question

EXERCISES Find an equation for the family of linear functions with slope 2 and sketch several members of the family. Find an equation for the family of linear functions such that f(2)=1 and sketch several members of the family. Which function belongs to both families? What do all members of the family of linear functions f(x) = 1 + m(x + 3) have in common? Sketch several members of the family. What do all members of the family of linear functions f(x) = c - x have in common? Sketch several members of the family. Find expressions for quadratic functions whose graphs are shown. Find an expression for a cubic function f if f(1) = 6 and f(-l) =f(0) =f(2) = 0. Some scientists believe that the average surface temperature of the world has been rising steadily. They have modeled the temperature by the linear function T = 0.02t + 8.50, where T is temperature in degree and t represents years since 1900

Explanation / Answer

The general equation of a quadratic equation is :
y = ax2+bx+c

now the equation passes through (4,2) and (3,0)

so,   

2= 16a + 4b +c -----------(1)

0= 9a + 3b +c -------------(2)

subtract (2) from (1),

2= 7a + b ----------(3)

now dy/dx =0 at x=3 as it touches the x axis

so, 2ax + b =0 at x=3

therefore, 6a + b =0........(4)

subtracting (4) from (3)

a=2

substituting in (4) we get,

b= -12

substituting a and b in 2 we get

c= -18

equation is 2x2 -12x -18

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