Find a quadratic equation for a function y fxwhich crosses

Find a quadratic equation for a function y = f(x)|which crosses the x-axis at x = 5| and x = 2|, and which crosses the y-axis at y = 20.| f(x) =|

Solution

Note: If x=a is a zero, then (x-a) is the corresponding factor of the polynomial.

It is given that x=5 an dx=2 crosses the x-axis.

It means x=5 and x=2 are the zeros of y =f(x).

So the corresponding factors of f(x) are x-5 and x-2.

So we can assume that

f(x) = a (x-5)(x-2)...(1), where \'a\' is a constant to be determined.

It is given that f(x) crosses y-axis at y=20.

It means that (0,20) =(x,y) is a point on (1). Substituting this in (1), we get

20 = a(0-5)(0-2)

20=10a

a =2

Substituting this in (1),

y = 2(x-5)(x-2) = 2(x²-5x-2x+10) = 2(x²-7x+10) = 2x²-14x+20

So f(x) =2x²-14x+20