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

1 Answer
Rachel
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 = (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

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