Question

Graph of a quadratic polynomial  is  in the shape of U .If the points ( -2 ,6) ,(  -1 0)

( 0, -4)   ( 1 ,-6)  (2,-6)   ( 4  ,0) and( 5,6)  lies on the graph.  Then the quadratic polynomial is -------

(help!) ​

Answer 1

Answer: y = (x + 1)*(x - 4)

Explanation:

The points of the equation are:

( -2 ,6), ( -1 0) , ( 0, -4) ( 1 ,-6) (2,-6) ( 4 ,0) and ( 5,6)

The first thing you can see is that the roots are:

( -1 0) and ( 4 ,0)

the roots are x1 = -1 and x2 = 4

and we know that we can write a polynomial as:

y = a*(x - x1)*(x - x2)

So our function can be:

y = a*(x - (-1))*(x - 4)

we also know that this graph passes trough the point (0, -4) so we can chek if this equation is correct:

y(0) = a*(0 + 1)*(0 - 4) = -4

a*1*-4 = -4

then y = (x + 1)*(x - 4)