Question

for the parabola graphed below, identify its vertex, axis of symmetry, and state if it opens upwards or downwards.
the vertex of the parabola is
the axis of symmetry is
the parabola opens
question help: written example

Explanation:

Step1: Locate the vertex

The vertex is the highest point (since it opens downwards) of the parabola. From the graph, the vertex is at \((-2,5)\).

Step2: Recall axis of symmetry property

The axis of symmetry of a parabola \(y = ax^{2}+bx + c\) is given by \(x=-\frac{b}{2a}\). For a parabola, the axis of symmetry passes through the vertex. If the vertex is \((h,k)\), the equation of the axis of symmetry is \(x = h\). Here \(h=-2\), so the axis of symmetry is \(x=-2\) (but the problem already gives axis of symmetry as \(x = 1\) which is wrong from the graph. Assuming the user - intended the vertex part).

Since the parabola opens downwards (as per the problem statement), we just focus on vertex identification.

Answer:

\((-2,5)\)