How do you graph the parabola #y= - 1/2 * x^2# using vertex, intercepts and additional points?

Answer 1

Look at the explanation section.

Given -

#y=-1/2x^2#

Since it has no constant term, Its vertex and intercept is #(0,0)#

Take a few points on either side of #x=0#. Find the corresponding #y# value.

Tabulate the va;ues.
Plot the pair of points.
Join all the points.
You get the parabola.

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Answer 2

To graph the parabola ( y = -\frac{1}{2}x^2 ), you can follow these steps:

  1. Vertex: The vertex of the parabola is at the point (0, 0).

  2. Intercepts:

    • 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).

    • 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).

  3. 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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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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