How do you graph the parabola #y = (x + 4)^2 - 3# using vertex, intercepts and additional points?

Answer 1

First: Notice the form
Second: Solve for the intercepts
Third: Pair up

Note that the given follows the form of opening up/down. Additonally, its form follows the opening up parabola since the given has a positive 'x' component. Also we now know that the vertex of the parabola is at (-4,-3). How? By rearranging the given, we can see the general form: • #y+3=(x+4)^2# • #y-(-3)=(x-(-4))^2#

Hence, the verex is at (-4,-3).

For the x-intercept, let #x =0#
#y=(0+4)^2-3# #y=16-3# #y=13#

Hence, the x-intercept is at (0,13).

Next is the y-intercept. Let #y=0#.
#0=(x+4)^2-3# #3=(x+4)^2# #±√3=x+4# #-4±√3=x# #x=-4±√3#

Hence, the y-intercepts are at (-4-√3,0) and (-4+√3,0).

Choose any number as your #x# and substitute it into the given equation. Then, pair the chosen #x#'s to their corresponding solution.
Example: Let #x=1#
#y=(1+4)^2-3# #y=5^2-3# #y=25-3# #y=22#

Thus, the pairing would be: (1,22). And so on.

Hope this helps!

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Answer 2

To graph the parabola ( y = (x + 4)^2 - 3 ):

  1. Vertex: The vertex is at (-4, -3).
  2. 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} ).
  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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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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