Question

which equation best matches the graph shown below?
answer
\\( y = 0.3(x - 3)^2 - 5 \\)
\\( y = 0.3(x + 3)^2 + 5 \\)
\\( y = 0.3(x - 3)^2 + 5 \\)
\\( y = 0.3(x + 3)^2 - 5 \\)

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is \( y=a(x - h)^2 + k \), where \((h,k)\) is the vertex of the parabola. If \(a>0\), the parabola opens upwards; if \(a<0\), it opens downwards.

Step2: Identify the vertex from the graph

Looking at the graph, the vertex (the lowest point of the parabola since it opens upwards) is at \((3, - 5)\). So \(h = 3\) and \(k=-5\).

Step3: Determine the value of \(a\)

The coefficient \(a\) here is \(0.3\) (positive, which matches the parabola opening upwards). Substituting \(h = 3\), \(k=-5\) and \(a = 0.3\) into the vertex form, we get \(y=0.3(x - 3)^2-5\).

Answer:

\( y = 0.3(x - 3)^2 - 5 \)