Question

use the graph of the parabola to fill in the table.
(a) does the parabola open upward or downward?
upward downward
(b) find the intercept(s).
for both the x - and y - intercept(s), make sure to do the following.

• if there is more than one, separate them with commas.
• if there are none, select

one\.
x - intercept(s):
y - intercept(s):
(c) find the coordinates of the vertex.
vertex: (, )
(d) find the equation of the axis of symmetry.
equation of axis of symmetry:

Explanation:

Step1: Determine the direction of the parabola

A parabola opens upward if the coefficient of \(x^{2}\) is positive and downward if the coefficient of \(x^{2}\) is negative. From the graph, the parabola has a "frown - like" shape, so it opens downward.

Step2: Find the x - intercepts

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

Step3: Find the y - intercept

The y - intercept is the point where \(x = 0\). By looking at the graph, when \(x = 0\), \(y=-3\).

Step4: Find the vertex

The vertex of a parabola is the highest (if it opens downward) or lowest (if it opens upward) point. From the graph, the vertex has coordinates \((1,1)\).

Step5: Find the axis of symmetry

The axis of symmetry of a parabola is a vertical line \(x = h\), where \((h,k)\) is the vertex of the parabola. Since the vertex is \((1,1)\), the equation of the axis of symmetry is \(x = 1\).

Answer:

A. downward
B. x - intercept(s): \(3, - 1\); y - intercept(s): \(-3\)
C. vertex: \((1,1)\)
D. equation of axis of symmetry: \(x = 1\)