Look at the graph and comment on the sign of D or the discriminant. Form the quadratic equation based on the information provided and find its solution.

And this is what I did

The sign of discriminant is positive because the parabola opens up, not down.

The x intercepts are -1, and 0.67

y = a(x - (-1) (x - 0.67)
y = a (x + 1) (x - 0.67)

lowest point of the parabola is the vertex
the parabola passes through - 0.16 and -2

-2 = a(-0.16 + 1) ( - 0.16 - 0.67)
-2 = a(0.84) (- 0.83)
a = -2/ (0.84)(- 0.83)
a = 2.87

the quadratic equation y = 2.87 ( x + 1) (x - 0.67)

2.87 ( x² + 0.33x - 0.67 ) = y

solve for x---equate y to 0

x² + 0.33x - 0.67 = 0
x² + 0.33x - 0.67 = 0
x² + x - 0.67 x - 0.67 = 0
x (x + 1) - 0.67 ( x + 1) = 0
(x + 1) (x - 0.67) = 0
x + 1 = 0 or x - 0.67 = 0
x = -1 or x = 0.67 (solution)

TEACHER SAID: the sign of the discriminant does not relate to whether it opens up or down

Can you help me come up with the sign of the discriminant. Isn't there some sort of formula (b²-4ac) or something? Please help me understand this. I am studying for a mid-term test and I need to understand. Please!! It would be real helpful if you could help me plug the numbers for the discriminant.