Question

find the y -intercept of $y = x^2 - 2x + 5$. options: 1, -2, 0, 5

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \( y = f(x) \) is the value of \( y \) when \( x = 0 \).

Step2: Substitute \( x = 0 \) into the equation

Given the equation \( y=x^{2}-2x + 5 \), substitute \( x = 0 \):
\( y=(0)^{2}-2(0)+5 \)

Step3: Simplify the expression

Simplify the right - hand side: \( y = 0 - 0+5=5 \).

Answer:

The y - intercept is 5, so the correct option is the one with 5 (the right - most option among the given ones with value 5).