Start by plotting the y-intercept at (0,1).
From that point, count "up 2, right 1" to get a second point on your graph.
If needed repeat that "up 2, right 1" from that second point to get a third point.
Draw the line that connects these 2 or 3 points.
F(x)=x^3+2
we see the power is odd
the ends go in opsoite directions
we know that if the leadind coefient (number in front of highest power term) is positive, then odd powered polynomials go from bottom left to top right
and for even ones, it goes both up
for negative, odd ones go from top left to bottom right
for even, both go down
we gots
f(x)=1x^3+2
positive and odd, so it goes from bottom left to top right
as x approaches negative inifnity, y approaches negaitve infinity
as x approaches infinity, y approaches infinity
Answer:
- vertex (3, -1)
- y-intercept: (0, 8)
- x-intercepts: (2, 0), (4, 0)
Step-by-step explanation:
You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.
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<h3>Vertex</h3>
The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).
<h3>Y-intercept</h3>
The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).
<h3>X-intercepts</h3>
The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).
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<em>Additional comment</em>
The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.
