How do you use the important points to sketch the graph of #f(x) = 1/3(x + 5)^2  1#?
See explanation
Set:
Compare the graph to the given equation.
Observe that
To find the
To find the
Mark the points on the axis then draw free hand the best curve you can that passes through these points. Do this remembering that the axis of symmetry is at
Solve
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To sketch the graph of ( f(x) = \frac{1}{3}(x + 5)^2  1 ), follow these steps:

Identify the vertex: The vertex of the parabola represented by the function ( f(x) ) is given by the coordinates ((5, 1)).

Determine the direction of opening: Since the coefficient of ( x^2 ) is positive (( \frac{1}{3} )), the parabola opens upwards.

Find the yintercept: Substitute ( x = 0 ) into the equation to find the yintercept. ( f(0) = \frac{1}{3}(0 + 5)^2  1 = \frac{1}{3}(5)^2  1 = \frac{25}{3}  1 = \frac{22}{3} ). So, the yintercept is ( (0, \frac{22}{3}) ).

Plot additional points: Choose additional xvalues, plug them into the equation, and calculate corresponding yvalues to plot more points if needed.

Sketch the graph: Use the vertex, direction of opening, and plotted points to sketch the graph of the function.

Label the vertex and any other significant points on the graph.

Draw the parabola through the plotted points, ensuring it opens upwards and has its vertex at ((5, 1)).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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