Question

for the function $f(x) = x^2 - 2x + 5$, the vertex is located at which point?
a. $(-1, 4)$
b. $(2, 5)$
c. $(1, 4)$
d. $(0, 5)$

Explanation:

Step1: Recall vertex formula for quadratic

For \( f(x)=ax^2 + bx + c \), vertex x - coordinate is \( x = -\frac{b}{2a} \).
Here, \( a = 1 \), \( b = -2 \), so \( x = -\frac{-2}{2\times1}=1 \).

Step2: Find y - coordinate of vertex

Substitute \( x = 1 \) into \( f(x)=x^2 - 2x + 5 \).
\( f(1)=1^2 - 2\times1 + 5=1 - 2 + 5 = 4 \).
So vertex is \( (1, 4) \).

Answer:

c. (1, 4)