How to graph a parabola #y = (x - 2)^2 + 1#?

Answer 1

See below

First, graph the parent function #y=x^2#

graph{x^2 [-10, 10, -5, 5]}

Then, we transform the graph based on the problem. The #-2# on the inside signifies a shift to the right by #2#. The 1 on the outside signifies a shift upward by 1. So our graph becomes more like:

graph{((x-2)^2)+1 [-10, 10, -1, 9]}

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Answer 2

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

  1. Identify the vertex of the parabola, which is the point (h, k) in the equation y = a(x - h)^2 + k. In this case, the vertex is (2, 1).

  2. Plot the vertex on the coordinate plane.

  3. Since the coefficient a is positive, the parabola opens upwards.

  4. Choose additional points on either side of the vertex and plot them. For example, if you choose x = 0, you get y = (0 - 2)^2 + 1 = 4 + 1 = 5. So the point (0, 5) is on the parabola.

  5. Plot the additional points and draw a smooth curve through them to complete the graph of the parabola.

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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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