Question

what are the solutions to the quadratic function: $y = x^2 - 4x + 5$

Explanation:

Step1: Identify quadratic coefficients

For $y=x^2-4x+5$, $a=1$, $b=-4$, $c=5$

Step2: Use quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Calculate discriminant

$b^2-4ac=(-4)^2-4(1)(5)=16-20=-4$

Step4: Substitute and simplify

$$x=\frac{4\pm\sqrt{-4}}{2}=\frac{4\pm2i}{2}=2\pm i$$

Answer:

$2 \pm i$