Question

Dear Ms. Quadratic

I followed all of the directions given in your
brochure on how to order a parabola. I tried to
order a parabola that is passed through the points
(1,0) and (-6,0)

Answer 1

We have the parabola as;

x^2 + 5x - 6

Explanation:

Here, we want to get a parabola that passes through the points (1,0) and (-6,0)

The general form of a quadratic equation is;

y = ax^2 + bx + c

We have two x-intercepts at x = 1 and x = -6

A quadratic equation is expected to have two roots only and that means we have these two values as the roots

Hence, we have ;

(x-1) and (x + 6)

The parabola is thus;

(x-1)(x + 6)

= x(x + 6) -1(x + 6)

= x^2 + 6x - x -6

= x^2 + 5x - 6