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 coordinates of the vertex.
vertex: ( , )
(c) find the equation of the axis of symmetry.
equation of axis of symmetry:
(d) 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):

Explanation:

Step1: Determine the direction of the parabola

By observing the graph, the parabola opens downward.

Step2: Find the vertex coordinates

The vertex is the highest point of the parabola. From the graph, the vertex coordinates are \((3, - 1)\).

Step3: Find the equation of the axis of symmetry

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

Step4: Find the \(x\)-intercepts

The \(x\)-intercepts are the points where \(y = 0\). From the graph, the \(x\)-intercepts are \((1,0)\) and \((5,0)\).

Step5: Find the \(y\)-intercept

The \(y\)-intercept is the point where \(x = 0\). From the graph, the \(y\)-intercept is \((0,-10)\).

Answer:

(a) downward
(b) \((3,-1)\)
(c) \(x = 3\)
(d) \(x\)-intercept(s): \((1,0),(5,0)\); \(y\)-intercept(s): \((0,-10)\)