Question

question 4 of 14 use the graph of the parabola to fill in the table. (a) does the parabola open upward or downward? upward downward (b) find the coordinates of the vertex. vertex: ( ) (c) find the equation of the axis of symmetry. equation of axis of symmetry: ( ) (d) find the intercept(s). x - intercept(s): ( ) y - intercept(s): ( )

Explanation:

Step1: Observe the parabola shape

The parabola opens downward as it has a peak and the branches go downwards.

Step2: Locate the vertex

The vertex is the highest point of the parabola. By observing the graph, the vertex is at the point (- 1,2).

Step3: Determine axis - of - symmetry

The axis of symmetry is a vertical line passing through the vertex. For a point \((x,y)\) at the vertex, the equation of the axis of symmetry is \(x = x\)-coordinate of the vertex. So the equation of the axis of symmetry is \(x=-1\).

Step4: Find \(x\) - intercepts

The \(x\)-intercepts are the points where the parabola crosses the \(x\)-axis (\(y = 0\)). By observing the graph, the \(x\)-intercepts are approximately \(x=-3\) and \(x = 1\).

Step5: Find \(y\) - intercept

The \(y\)-intercept is the point where the parabola crosses the \(y\)-axis (\(x = 0\)). By observing the graph, the \(y\)-intercept is \(y = 0\).

Answer:

(a) downward
(b) (-1,2)
(c) \(x=-1\)
(d) \(x\)-intercept(s): - 3,1; \(y\)-intercept(s): 0