How do you graph #f(x)=1/2x^2 +2x - 8#?
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For plotting a function, assume values for x, calculate f(x). Plot(x,f(x)) in rectangular coordinates.
graph{1/2x^2+2x-8 [-10, 10, -5, 5]}
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To graph the function (f(x) = \frac{1}{2}x^2 + 2x - 8), you can follow these steps:
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Identify the vertex of the parabola using the formula (x = -\frac{b}{2a}), where (a = \frac{1}{2}) (the coefficient of (x^2)) and (b = 2) (the coefficient of (x)). Calculate the x-coordinate of the vertex: (x = -\frac{2}{2 \times \frac{1}{2}} = -2). Then, substitute (x = -2) into the function to find the corresponding y-coordinate: (f(-2) = \frac{1}{2}(-2)^2 + 2(-2) - 8 = -6). So, the vertex is at the point ((-2, -6)).
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Find additional points to plot by choosing x-values around the vertex. You can use symmetry to find points on either side of the vertex. For example, when (x = -3), (f(-3) = \frac{1}{2}(-3)^2 + 2(-3) - 8 = -\frac{11}{2}). And when (x = -1), (f(-1) = \frac{1}{2}(-1)^2 + 2(-1) - 8 = -\frac{9}{2}).
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Plot the vertex and the additional points on the graph.
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Since the coefficient of (x^2) is positive ((\frac{1}{2})), the parabola opens upwards. Connect the plotted points smoothly to form the graph of the function.
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Optionally, you can label the vertex and any other key points on the graph for clarity.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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