Question

The first equation in the system presented here represents the path of the sailboat. The second equation represents the path of the motorboat.

y = −0.5(x − 2)2 + 0.5
y = 0.5(x + 1)2 − 1.5
You used substitution to obtain the equation 0 = x2 − x + 0.5 from the system. How many real solutions does the system have?

Answer 1

o real solutions

Explanation:

Answer 2

The system has no real solutions.

We use the discriminant to determine how many solutions it has:
b²-4ac

This is the value under the square root in the quadratic formula. If this value is negative, then there is no real solution; we cannot have a real number square root of a negative value.
If this value is 0, there is one real solution, and if this value is positive, there are 2 real solutions.

b²-4ac=(-1)²-4(1)(0.5)=1-2=-1