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 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): (d) find the coordinates of the vertex. vertex:

Explanation:

Step1: Determine parabola opening direction

Observe the graph. Since the parabola has a U - shape, it opens upward.

Step2: Find axis of symmetry

The axis of symmetry of a parabola passes through the vertex. From the graph, the x - coordinate of the vertex is 2. So the equation of the axis of symmetry is $x = 2$.

Step3: Find x - intercepts

The x - intercepts are the points where the parabola crosses the x - axis. From the graph, the x - intercepts are $x=-2$ and $x = 6$.

Step4: Find y - intercept

The y - intercept is the point where the parabola crosses the y - axis. From the graph, the y - intercept is $y=-4$.

Step5: Find vertex coordinates

From the graph, the vertex of the parabola is at the point $(2,-4)$.

Answer:

(a) upward
(b) $x = 2$
(c) x - intercept(s): $-2,6$; y - intercept(s): $-4$
(d) $(2,-4)$