Question

which equation best matches the graph shown below?
answer
$y = -0.6x^2 - 2x + 9$
$y = -0.6x^2 - 2x + 7.3$
$y = 0.6x^2 - 2x + 7.3$
$y = 0.6x^2 - 2x + 9$

Explanation:

Step1: Analyze the parabola's direction

The parabola opens upwards, so the coefficient of \(x^2\) (let's call it \(a\)) must be positive. So we can eliminate the options with \(a = -0.6\) (the first two options: \(y=-0.6x^2 - 2x + 9\) and \(y=-0.6x^2 - 2x + 7.3\)).

Step2: Analyze the y - intercept

The y - intercept is the value of \(y\) when \(x = 0\). From the graph, when \(x = 0\), \(y\) is approximately 9 (since the graph crosses the y - axis at \(y\approx9\)). Now we check the remaining two options:

• For \(y = 0.6x^2-2x + 7.3\), when \(x = 0\), \(y=7.3\).
• For \(y = 0.6x^2-2x + 9\), when \(x = 0\), \(y = 9\).

So the equation \(y = 0.6x^2-2x + 9\) matches the direction of the parabola (upwards) and the y - intercept.

Answer:

\(y = 0.6x^2-2x + 9\)