Question

select the correct answer.

which equation best fits the graphed data?

\\(y = -3x^2 + 0.6x - 1\\)

\\(y = 3x - 1\\)

\\(y = -\frac{1}{2}x^2 + 0.6x - 1\\)

\\(y = -\frac{3}{5}x - 4\\)

Explanation:

Identify the shape and key features of the graphed data

The plotted points form a downward-opening parabola, indicating a quadratic relationship of the form \(y = ax^2 + bx + c\) with \(a < 0\).

Analyze the vertex and y-intercept

The vertex of the parabola is located near \((0.6, -1)\), and the y-intercept is at \((0, -1)\).

Evaluate the given options at key points

For \(y = -3x^2 + 0.6x - 1\):
At \(x = 2\), \(y = -3(4) + 0.6(2) - 1 = -12 + 1.2 - 1 = -11.8\).
However, the graph shows that at \(x = 2\), \(y = -2\).

For \(y = -\frac{1}{2}x^2 + 0.6x - 1\):
At \(x = 2\), \(y = -\frac{1}{2}(4) + 0.6(2) - 1 = -2 + 1.2 - 1 = -1.8 \approx -2\).
At \(x = -2\), \(y = -\frac{1}{2}(4) + 0.6(-2) - 1 = -2 - 1.2 - 1 = -4.2 \approx -4\).
These values closely match the plotted points \((2, -2)\) and \((-2, -4.3)\).

Answer:

• (A) \(y = -3x^2 + 0.6x - 1\)
• (B) \(y = 3x - 1\)</mcq-correct>
• (C) \(y = -\frac{1}{2}x^2 + 0.6x - 1\) (Correct answer)

<mcq-option>(D) \(y = -\frac{3}{5}x - 4\)