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

By observing the graph, the parabola opens upward.

Step2: Find the x - intercept(s)

The x - intercept is the point where the graph crosses the x - axis. From the graph, the parabola touches the x - axis at \(x = 3\). So, the x - intercept is \(3\).

Step3: Find the y - intercept(s)

The y - intercept is the point where the graph crosses the y - axis. From the graph, when \(x = 0\), \(y=5\). So, the y - intercept is \(5\).

Step4: Find the vertex of the parabola

The vertex of a parabola is the lowest (if it opens upward) or highest (if it opens downward) point on the graph. From the graph, the vertex is \((3,0)\).

Step5: Find the equation of the axis of symmetry

The axis of symmetry of a parabola passes through the vertex. For a parabola with vertex \((h,k)\), the equation of the axis of symmetry is \(x = h\). Here, \(h = 3\), so the equation of the axis of symmetry is \(x = 3\).

Answer:

(a) upward
(b) \(x\) - intercept(s): \(3\); \(y\) - intercept(s): \(5\)
(c) vertex: \((3,0)\)
(d) equation of axis of symmetry: \(x = 3\)