How do you graph the parabola #y= - 1/2 * x^2# using vertex, intercepts and additional points?
Look at the explanation section.
Given -
#y=-1/2x^2#
Since it has no constant term, Its vertex and intercept is Take a few points on either side of Tabulate the va;ues.
Plot the pair of points.
Join all the points.
You get the parabola.
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To graph the parabola ( y = -\frac{1}{2}x^2 ), you can follow these steps:
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Vertex: The vertex of the parabola is at the point (0, 0).
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Intercepts:
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x-intercept: Set ( y = 0 ) and solve for ( x ). [ 0 = -\frac{1}{2}x^2 ] [ x = 0 ] So, the x-intercept is at (0, 0).
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y-intercept: Set ( x = 0 ) and solve for ( y ). [ y = -\frac{1}{2}(0)^2 ] [ y = 0 ] So, the y-intercept is also at (0, 0).
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Additional Points: You can choose additional points by substituting different values of ( x ) into the equation to get corresponding ( y ) values. For example, when ( x = 1 ): [ y = -\frac{1}{2}(1)^2 = -\frac{1}{2} ] So, an additional point is (1, -0.5).
Plotting these points and using the symmetry of the parabola, you can sketch the graph.
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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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