How do you graph the parabola #y= 5/4(x+2)^2 -1# using vertex, intercepts and additional points?
Vertex: Y-intercept: X-intercepts:
Graph:
where:
Note: This is a long process.
Simplify.
Take the square root of both sides.
Simplify.
Simplify.
Switch sides.
Summary:
Plot the points and sketch a parabola through the points. Do not connect the dots.
graph{y=5/4(x+2)^2-1 [-10, 10, -5, 5]}
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To graph the parabola (y = \frac{5}{4}(x + 2)^2 - 1), follow these steps:
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Vertex: The vertex form of a parabola is (y = a(x - h)^2 + k), where ((h, k)) is the vertex. In this case, the vertex is ((-2, -1)).
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Intercepts:
- y-intercept: Set (x = 0) and solve for (y). (y = \frac{5}{4}(0 + 2)^2 - 1 = \frac{5}{4}(4) - 1 = 5 - 1 = 4). So, the y-intercept is ((0, 4)).
- x-intercept: Set (y = 0) and solve for (x). (0 = \frac{5}{4}(x + 2)^2 - 1). Solve for (x) to find the x-intercepts.
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Additional Points: Choose additional values of (x) to calculate corresponding (y) values. For instance, choose (x = -3, -1, 1) and find the corresponding (y) values.
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Plot the vertex, intercepts, and additional points on the coordinate plane. Draw the parabola passing through these points.
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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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