Question

quadratic relationships
24
select the correct ans
select the graph of the equa
$y = -\frac{1}{4}x^2 + 1$
a.
graph a

b.
graph b

c.
graph c

d.
graph d

Explanation:

Step1: Analyze the quadratic function

The given function is \( y = -4x^2 + 1 \). For a quadratic function in the form \( y = ax^2 + bx + c \), the coefficient \( a \) determines the direction the parabola opens. Here, \( a=-4 \), which is negative, so the parabola opens downward.

Step2: Find the vertex

The vertex of a quadratic function \( y = ax^2 + c \) (since \( b = 0 \) here) is at \( (0, c) \). For \( y=-4x^2 + 1 \), \( c = 1 \), so the vertex is at \( (0, 1) \).

Step3: Analyze the options

• Option A: The parabola opens downward and has a vertex at \( (0, 1) \), which matches our analysis.
• Option B: The parabola opens downward but the vertex is not at \( (0, 1) \), so it's incorrect.
• Option C: The parabola opens upward (since \( a \) would be positive), which contradicts \( a=-4 \), so incorrect.
• Option D: The parabola opens upward and the vertex is not at \( (0, 1) \), so incorrect.

Answer:

A. The graph with a downward - opening parabola and vertex at (0, 1)