Question

module 4 - practice quiz (ch 7) quadratic equations and functions
question 10 of 10 (1 point) | question attempt: 1 of unlimited
y₁ = 4x² - 4x + 5
part 1 of 2
the vertex is (0.5, 4).
part: 1 / 2
part 2 of 2
graphs of quadratic functions labeled a, b, c, d

Explanation:

Step1: Analyze the quadratic function

The function is \( Y_1 = 4x^2 - 4x + 5 \). The coefficient of \( x^2 \) is \( 4>0 \), so the parabola opens upward. The vertex is \( (0.5, 4) \) (from Part 1).

Step2: Analyze each graph

• Graph A: Opens downward (coefficient of \( x^2 \) negative), so eliminate.
• Graph B: Vertex at \( (0, 5) \), but our vertex is \( (0.5, 4) \), so eliminate.
• Graph C: Opens downward, eliminate.
• Graph D: Opens upward, and let's check the vertex. The vertex \( x \)-coordinate is \( 0.5 \) (midway between \( 0 \) and \( 1 \)) and \( y \)-coordinate around \( 4 \), which matches. Also, the shape and vertex position fit \( Y_1 = 4x^2 - 4x + 5 \).

Answer:

The graph labeled D (the bottom - right graph)