How do you find the vertex and intercepts for #y=2(x+2)^2+3#?
Vertex is at
graph{2(x+2)^2+3 [-40, 40, -20, 20]} [Ans]
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To find the vertex and intercepts for the quadratic function y = 2(x + 2)^2 + 3:
-
Find the vertex:
- The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex.
- Comparing the given function to the vertex form, we can see that h = -2 and k = 3.
- Therefore, the vertex is (-2, 3).
-
Find the x-intercepts (zeros):
- To find the x-intercepts, set y = 0 and solve for x.
- 0 = 2(x + 2)^2 + 3
- Solve for (x + 2)^2 = -3/2. Since a square cannot be negative, there are no real solutions, indicating no x-intercepts.
-
Find the y-intercept:
- To find the y-intercept, set x = 0 and solve for y.
- y = 2(0 + 2)^2 + 3
- y = 2(4) + 3
- y = 8 + 3
- y = 11
- Therefore, the y-intercept is (0, 11).
The vertex is (-2, 3), and the y-intercept is (0, 11). There are no x-intercepts.
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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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