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 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 equation of the axis of symmetry. equation of axis of symmetry:

Explanation:

Step1: Observe the parabola shape

By looking at the graph, we can see the parabola opens upward.

Step2: Locate the vertex

The vertex is the lowest point of the parabola. From the graph, it is at the point $(4, 0)$.

Step3: Find x - intercepts

The x - intercepts are the points where the parabola crosses the x - axis. The parabola touches the x - axis at $x = 4$, so the x - intercept is $4$.

Step4: Find y - intercepts

The y - intercept is the point where the parabola crosses the y - axis. From the graph, it is at the point $(0, 8)$.

Step5: Determine 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 $h = 4$, so the equation of the axis of symmetry is $x = 4$.

Answer:

(a) upward
(b) $(4,0)$
(c) x - intercept(s): $4$; y - intercept(s): $8$
(d) $x = 4$