A parabola has been transformed from \(y=x^2\) by reflecting over the \(x\)-axis, stretching vertically by a factor of 4, shifting down 7, and shifting left 3. 

1. What is an equation for this parabola?
2. What is the vertex of this parabola?

What transformations will take the parabola \(y=x^2\) to the parabola \(y=\frac53(x-13)^2+12\)?

A parabola is transformed from \(y=x^2\) to \(y=\text-4x^2-16x-24\). 

1. Write an equation for the parabola in vertex form. 
2. What transformations were applied to the parabola?

Draw the graph of the new function after the following transformations:

1. Function \(g\) has been translated right 2, stretched vertically by a factor of \(\frac13\), and translated down 5.
2. Function \(h\) has been reflected over the \(x\)-axis, stretched horizontally by a factor of 2, and translated up 2.
3. Function \(k\) has been stretched horizontally by a factor of 2, shifted left 4, and shifted up 4.

Describe the transformation from \(f(x)\) to \(g(x)\) if \(f(x)=e^x\) and \(g(x)\) is equal to:

1. \(e^{(\text-2x)}+3\)
2. \(\frac13e^{3x}-5\)
3. \(5e^{(\text-2x)}\)

Match each function with the transformation that describes it.