Determine if y=2(x-3)^2 +6 a function by graphing.
To determine if y=2(x-3)^2 +6 is a function by graphing, we would need to see if there are any points on the graph where a vertical line intersects the graph at more than one point.
To graph the equation, we can start by finding some key points. We can do this by assigning values to x and solving for y.
Let's start by plugging in x=0:
y = 2(0-3)^2 + 6
y = 2(-3)^2 + 6
y = 2(9) + 6
y = 18 + 6
y = 24
So, when x=0, y=24. One point on the graph is (0, 24).
Now let's plug in x=1:
y = 2(1-3)^2 + 6
y = 2(-2)^2 + 6
y = 2(4) + 6
y = 8 + 6
y = 14
When x=1, y=14. Another point on the graph is (1, 14).
We can continue this process to find more points on the graph.
Let's plug in x=2:
y = 2(2-3)^2 + 6
y = 2(-1)^2 + 6
y = 2(1) + 6
y = 2 + 6
y = 8
When x=2, y=8. Another point on the graph is (2, 8).
Let's plug in x=3:
y = 2(3-3)^2 + 6
y = 2(0)^2 + 6
y = 2(0) + 6
y = 6
When x=3, y=6. Another point on the graph is (3, 6).
We can continue this process to find more points, but let's plot the points we have so far:
(0, 24)
(1, 14)
(2, 8)
(3, 6)
As we can see from the graph, when we draw a vertical line through any point on the graph, it only intersects the graph at that one point. Therefore, the graph satisfies the vertical line test and y=2(x-3)^2 +6 is a function.
Here is the plotted graph:
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