Question

which equation best matches the graph shown below?
answer
\\( y = -0.4x^2 + x - 2 \\) \\( y = -0.4x^2 + x - 2.6 \\)
\\( y = 0.4x^2 + x - 2 \\) \\( y = 0.4x^2 + x - 2.6 \\)

Explanation:

Step1: Analyze the parabola's direction

The graph opens upwards, so the coefficient of \(x^2\) must be positive. Eliminate options with \(-0.4x^2\) (first two options).

Step2: Check the y-intercept

The graph crosses the y - axis at \(y\approx - 2.6\). Now check the remaining options:

• For \(y = 0.4x^2+x - 2\), the y - intercept is \(-2\).
• For \(y = 0.4x^2+x - 2.6\), the y - intercept is \(-2.6\), which matches the graph.

Answer:

\(y = 0.4x^2+x - 2.6\) (the fourth option: \(y = 0.4x^2 + x - 2.6\))