How do you graph the parabola #y = (x + 4)^2 - 3# using vertex, intercepts and additional points?
First: Notice the form
Second: Solve for the intercepts
Third: Pair up
Hence, the verex is at (-4,-3).
Hence, the x-intercept is at (0,13).
Hence, the y-intercepts are at (-4-√3,0) and (-4+√3,0).
Thus, the pairing would be: (1,22). And so on.
Hope this helps!
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To graph the parabola ( y = (x + 4)^2 - 3 ):
- Vertex: The vertex is at (-4, -3).
- Intercepts:
- Y-intercept: Substitute ( x = 0 ) into the equation to find the y-intercept, which is ( y = 13 ).
- X-intercept: Set ( y = 0 ) and solve for ( x ) to find the x-intercept. ( (x + 4)^2 - 3 = 0 ) which simplifies to ( (x + 4)^2 = 3 ). Taking the square root of both sides gives ( x + 4 = \pm \sqrt{3} ), so ( x = -4 \pm \sqrt{3} ).
- Additional Points: Choose additional points and evaluate them using the equation. For example, you can choose points to the left and right of the vertex. Let's say ( x = -6 ) and ( x = -2 ). Substitute these values into the equation to find their corresponding y-values:
- For ( x = -6 ), ( y = (-6 + 4)^2 - 3 = 1 ), giving the point (-6, 1).
- For ( x = -2 ), ( y = (-2 + 4)^2 - 3 = 1 ), giving the point (-2, 1).
Plot these points and sketch the parabola passing through them.
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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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