How do you solve #1/3x^2 - 3=0# by graphing?

Answer 1

Refer the Explanation section

Given -

#1/3 x^2-3=0#

We shall have it as -

#y=1/3 x^2-3#

To graph the function, we must have the range of x values the includes solutions.

Find the two x-intercepts first

At #y=0; 1/3x^2-3=0#

#x^2=-=3 xx 3/1=9#

#x=+-sqrt9#
#x=3#
#x=-3#

The curve cuts the x-axis at #(3,0);(-3,0)#

Now take #x# values ranging from # 5 # to # -5#
Find the corresponding #y# values.

Then plot these values on a graph sheet.

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Answer 2

Plot the graph of #f(x) = 1/3x^2-3#. Solutions for #x# are found where #f(x)# intercepts the #x-#axis. #x=+-3#

The graph of #f(x) = 1/3x^2-3# is shown below.

graph{1/3x^2-3 [-3.51, 3.513, 7.023, 7.024]}

From this graph we can observe the #f(x)=0# for #x=+-3#

Thus, this concludes our response to your query.

Naturally, we can demonstrate this observation by solving the equation algebraically.

#1/3x^2-3=0 -> 1/3x^2 = 3#
#:.x^2=3xx3 = 9#
#x=sqrt9 =+-3#
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Answer 3

To solve ( \frac{1}{3}x^2 - 3 = 0 ) by graphing, follow these steps:

  1. Rewrite the equation as ( \frac{1}{3}x^2 = 3 ).
  2. Multiply both sides by 3 to get ( x^2 = 9 ).
  3. Take the square root of both sides to solve for x, giving you ( x = \pm 3 ).
  4. Plot the points (3, 0) and (-3, 0) on the graph.
  5. Draw a parabolic curve passing through these points. The curve represents the solutions to the equation ( \frac{1}{3}x^2 - 3 = 0 ).
  6. The x-intercepts of the curve at ( x = 3 ) and ( x = -3 ) are the solutions to the equation.
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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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