How do you graph #f(x)=1/2x^2 +2x - 8#?

Answer 1

Solve

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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Answer 2

To graph the function (f(x) = \frac{1}{2}x^2 + 2x - 8), you can follow these steps:

  1. 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)).

  2. 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}).

  3. Plot the vertex and the additional points on the graph.

  4. 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.

  5. Optionally, you can label the vertex and any other key points on the graph for clarity.

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Answer from HIX Tutor

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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