Find the equation of the line tangent to the graph of \( f(x)=3 x^{2}-7 \) at \( x=2 \). Use the point-slope form. Include a multiplication sign between symbols. For example, \( a^{*} x \).

To find the equation of the tangent line, we first need the derivative of \( f(x) = 3 x^{2} - 7 \). The derivative, \( f'(x) \), is calculated as follows: \[ f'(x) = 6 x. \] Next, we evaluate the derivative at \( x = 2 \): \[ f'(2) = 6 \times 2 = 12. \] This means the slope of the tangent line at \( x = 2 \) is \( 12 \). Now, we calculate \( f(2) \): \[ f(2) = 3 \times (2^{2}) - 7 = 3 \times 4 - 7 = 12 - 7 = 5. \] Now we have a point on the tangent line, \( (2, 5) \), and the slope \( 12 \). The point-slope form of the line is given by: \[ y - y_{1} = m \times (x - x_{1}), \] where \( m \) is the slope and \( (x_{1}, y_{1}) \) is the point. Substituting in our values: \[ y - 5 = 12 \times (x - 2). \] This is the equation of the tangent line in point-slope form!