To determine the number of solutions for the quadratic equation \( y = -x^2 + 4x - 5 \), we need to analyze it by using the discriminant method. The general form of a quadratic equation is \( ax^2 + bx + c = 0 \), where:
- \( a = -1 \)
- \( b = 4 \)
- \( c = -5 \)
The discriminant \( D \) is calculated using the formula:
\[ D = b^2 - 4ac \]
Substituting the values:
\[ D = 4^2 - 4 \cdot (-1) \cdot (-5) = 16 - 20 = -4 \]
Since the discriminant \( D \) is negative (\( D = -4 \)), this indicates that there are no real number solutions to the quadratic equation.
Therefore, the answer is:
No real number solutions.
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