write an equation

Question

Write the equation for the quadratic that contains the following points.

(-7,-265), (0,-6), (6,-96)

Answer 1

Let the quadratic be q(x)=ax²+bx+c where a, b and c are constants.

q(-7)=-265=49a-7b+c,

q(0)=-6=c, so c=-6,

q(6)=-96=36a+6b+c.

Since we know c=-6 we have a pair of equations with two unknowns:

49a-7b-6=-265⇒49a-7b=-259⇒7a-b=-37 (1)

36a+6b-6=-96⇒36a+6b=-90⇒6a+b=-15 (2)

(1)+(2)=13a=-52, a=-4.

6a+b=-24+b=-15, b=9.

q(x)=-4x²+9x-6 is the quadratic.