use the graph of the parabola to fill in the table. (a) does the parabola open upward or downward? upward…
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 \none\. x -intercept(s): y -intercept(s): (d) find the coordinates of the vertex. vertex:
Answer
Explanation:
Step1: Determine opening direction
Observe the graph. The parabola has a U - shape, so it opens upward.
Step2: Find axis of symmetry
The axis of symmetry of a parabola is a vertical line passing through the vertex. From the graph, the vertex is at (x = 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 parabola crosses the x - axis at (x = 0) and (x = 4).
Step4: Find y - intercepts
The y - intercept is the point where the parabola crosses the y - axis. From the graph, the parabola crosses the y - axis at (y = 0).
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): (0,4); (y)-intercept(s): (0) (d) ((2,-4))