Solve by graphing: y=3(x-2)^2-3

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Step 1: Identify a, h, and k.
a=3, h=2, k=-3

Step 2: Plot the vertex at (2,-3).

Step 3: The axis of symmetry is the line
x = 2

Step 4: Evaluate the function at two other x-values:
When x = 1, y = 0
When x = 0, y = 9

Step 5: Plot the points (1, 0) and (0, 9)

Step 6: use the property of symmetry to plot to more corresponding points on the right side of the vertical line.
{Plot (3, 0) and (4, 9)}

Step 7: Identify the zeros of the graph.
The roots of the equation are 1 and 3.


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Answer:

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Step-by-step explanation:

The required graphing of the function is shown in the image.


Given that,
To explains the property of the graph [tex]y=3(x-2)^2-3[/tex] , with help of the graph.

What is a graph?

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation [tex]y =4ax^2[/tex] .

Given expression is of parabola,
[tex]y=3(x-2)^2-3[/tex]
Properties are given by,

1 ) Vertex of the parabola
 (h, k) = (2, -3)

2) The axis of symmetry,
 x = 2

3)  Coordinate the focus
    (h, k+ 1/4a) = (2 , -3 + 1/4*3)
                       =  (2 , -2.91 )
4) The roots of the equation

  [tex]0 =3(x-2)^2-3\\[/tex]
  x - 2 = ± 1
  x = -1 and x = 3

Thus, the required graphing of the function is shown in the image.

Learn more about graphs here:

brainly.com/question/16608196

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