How many four-digit numbers can you form from the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 (a) if you use each digit only once? (b)
1 answer:
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Answer:
- The graph is shown below
- Vertex = (2,1)
- Axis of symmetry is x = 2
- Domain = set of all real numbers
- Range = set of y values such that
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Explanation:
Use your favorite graphing tool to graph the equation. If your teacher doesn't allow you to use graphing software, then you'll have to plug in various x values to find the paired y values. This gives the set of (x,y) points needed to be plotted to form the parabola. The more points you plot, the more accurate the curve.
The graph is shown below. I used GeoGebra to make the graph. It's free graphing software. Desmos is another tool that I recommend.
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The lowest point on the parabola is the vertex (h,k) = (2,1) which is shown in the graph below.
This is due to the equation being in vertex form y = a(x-h)^2 + k. We see that h = 2 and k = 1.
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The axis of symmetry is the vertical line that passes through the vertex.
As such, the axis of symmetry equation is simply x = h. So that's how we get to x = 2.
In the graph below, the axis of symmetry is the red dashed line.
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There aren't any restrictions on x. We don't have to worry about dividing by zero or applying a square root to a negative number.
Therefore, any x value is allowed and the domain is the set of all real numbers.
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The range however isn't the set of all real numbers. The lowest y can get is y = 1 due to the vertex point. We can have y = 1 or larger
Therefore, is the range.
