commongraphs

commongraphs - xample 1 Graph . Solution This is a line in...

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xample 1 Graph . Solution This is a line in the slope intercept form In this case the line has a y intercept of (0, b ) and a slope of m . Recall that slope can be thought of as Note that if the slope is negative we tend to think of the rise as a fall. The slope allows us to get a second point on the line. Once we have any point on the line and the slope we move right by run and up/down by rise depending on the sign. This will be a second point on the line. In this case we know (0,3) is a point on the line and the slope is . So starting at (0,3) we’ll move 5 to the right ( i.e. ) and down 2 ( i.e. ) to get (5,1) as a second point on the line. Once we’ve got two points on a line all we need to do is plot the two points and connect them with a line. Here’s the sketch for this line. Example 2 Graph Solution
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There really isn’t much to this problem outside of reminding ourselves of what absolute value is. Recall that the absolute value function is defined as, The graph is then, Example 3 Graph . Solution This is a parabola in the general form. In this form, the x -coordinate of the vertex (the highest or lowest point on the parabola) is and we get the y -coordinate is . So, for our parabola the coordinates of the vertex will be. So, the vertex for this parabola is (1,4).
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We can also determine which direction the parabola opens from the sign of a . If a is positive the parabola opens up and if a is negative the parabola opens down. In our case the parabola opens down. Now, because the vertex is above the x -axis and the parabola opens down we know that we’ll have x -intercepts ( i.e. values of x for which we’ll have ) on this graph. So, we’ll solve the following. So, we will have x -intercepts at and . Notice that to make our life easier in the solution process we multiplied everything by -1 to get the coefficient of the positive. This made the factoring easier. Here’s a sketch of this parabola.
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commongraphs - xample 1 Graph . Solution This is a line in...

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