Question

1. ( y = x^2 - 4x + 5 )

a) graph a
b) graph b
c) graph c
d) graph d

Explanation:

Step1: Analyze the function \( y = x^2 - 4x + 5 \)

First, we can rewrite the quadratic function in vertex form. The vertex form of a quadratic function \( y = ax^2 + bx + c \) is \( y = a(x - h)^2 + k \), where \( h = -\frac{b}{2a} \) and \( k = y(h) \). For \( y = x^2 - 4x + 5 \), \( a = 1 \), \( b = -4 \), so \( h = -\frac{-4}{2\times1} = 2 \). Then \( k = (2)^2 - 4\times2 + 5 = 4 - 8 + 5 = 1 \). So the vertex is at \( (2, 1) \). Also, when \( x = 0 \), \( y = 0 - 0 + 5 = 5 \), so the y - intercept is \( (0, 5) \).

Step2: Analyze the graphs

• For graph A: The vertex and y - intercept do not match the calculated values.
• For graph B: The vertex seems to be around \( (2, 1) \) and the y - intercept is around \( (0, 5) \), which matches our calculations.
• For graph C: The vertex and y - intercept do not match.
• For graph D: The vertex and y - intercept do not match.

Answer:

B (the graph labeled B)