Answer:
Positive
Step-by-step explanation:
In order to answer this question, we need to figure out the equation of the quadratic.
We see that the vertex is at (0, 4) and that the points (1, 3) and (2, 0) are on the graph. The generic quadratic is: ax^2 + bx + c, so we can just plug in these three points to find a, b, and c:
4 = 0 + 0 + c ⇒ c = 4
3 = a + b + c = a + b + 4 ⇒ a + b = -1
0 = 4a + 2b + c = 4a + 2b + 4 ⇒ 4a + 2b = -4
We now have two linear equations (a + b = -1 and 4a + 2b = -4) so multiply the first one by 2 and subtract it from the second:
4a + 2b = -4 ⇒ 4a + 2b = -4
- 2(a + b) = (-1) * 2 ⇒ - 2a + 2b = -2
______________ ⇒ ______________
Our difference is 2a = -2, so a = -1. Plug this back in to find b: a + b = -1.
-1 + b = -1
b = 0
So our equation is -x^2 + 4 = 0.
The discriminant is just b^2 - 4ac. Here, it is: 0^2 - 4 * (-1) * (4) = 16.
So the discriminant is positive.
Hope this helps!
