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

Jan 31, 2018

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

$y = {\left(x - 3\right)}^{2}$

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

Now up $4$ units

$y = {\left(x - 3\right)}^{2} + 4$

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

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

$y = 2 {\left(x - 3\right)}^{2} + 4$

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

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

$y = - 2 {\left(x - 3\right)}^{2} + 4$

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