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

A parabola opens downward if it has a maximum point (the vertex is the highest point). From the graph, the vertex is the peak, so it opens downward.

Step2: Find axis of symmetry

The axis of symmetry for a parabola is the vertical line through the vertex. The vertex's x - coordinate is - 5 (from the graph, the vertex is at x=-5), so the equation is \(x = - 5\).

Step3: Find vertex coordinates

The vertex is the highest point on the parabola. From the graph, the vertex is at \((-5, 2)\) (x=-5, y = 2).

Step4: Find x - intercepts

x - intercepts are where the parabola crosses the x - axis. From the graph, it crosses at \(x=-7\) and \(x=-3\) (so points \((-7,0)\) and \((-3,0)\)).

Step5: Find y - intercept

The y - intercept is where the parabola crosses the y - axis. From the graph, it crosses at \(y=-10\) (point \((0, - 10)\)).

Answer:

s:
(a) downward
(b) \(x=-5\)
(c) \((-5, 2)\)
(d) x - intercept(s): \(-7, - 3\); y - intercept(s): \(-10\)