Question

How do you sketch the graph of `y=-2(x-3)^2+4` and describe the transformation?

Answer 1

Let's work backwards. First we need to identify the parent function: `x^2`

graph{y=x^2}

Let's shift the graph to the right `3` units

`y = (x-3)^2`

graph{y=(x-3)^2}

Now up `4` units

`y=(x-3)^2+4`

graph{y=(x-3)^2+4}

Now we can stretch this by a factor of `2`

`y=2(x-3)^2+4`

graph{y=2(x-3)^2+4}

Our last step is to flip the graph across the `x`-axis

`y=-2(x-3)^2+4`

graph{y=-2(x-3)^2+4}

Does this graph look the same as the equation we were given?

graph{y=-2(x-3)^2+4}

Yep, so we shifted the parent function `x^2` to the right by `3` and up `4`, then stretches it by a factor of `2` and then flipped it over the `x`-axis