Find the quadratic polynomial whose graph goes through the points (-2,10), (0,6) and (1,10).  

Expert Answers
lemjay eNotes educator| Certified Educator

A quadratic polynomial has a form `y =ax^2+bx+c` .

To determine the value of a,b and c, plug-in the given points.

For (0,6), plug-in x=0 and y=6.



Hence, value of c is 6.
Now that value of c is known, plug-in this to the quadratic form of a polynomial.


Next, use (-2,10). Substitute x=-2 and y=10 to `y=ax^2+bx+c` .



Bring together the constants.



Divide both sides by 2, to simplify.


`2=2a-b`              (Let this be EQ1.)

Next, use (1,10). Substitute x=1 and y=10 to `y=ax^2+bx+6` .




4=a+b            (Let this be EQ2. )

To solve a and b, apply elimination method of system of equation.
So, add EQ1 and EQ2.


`(+)`     `4=a+b`


Then, plug-in a=2 to EQ1 to solve for b.








Now that values of a, b and c are know, plug-in these values to the quadratic form.



Hence, the quadratic polynomial is `y=2x^2+2x+6` .