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

1 Answer
Jan 9, 2018

See Explanation. Transformations are vertical stretch by a factor of 2, horizontal shift 4 units left, vertical shift 3 units down.

Explanation:

This is a quadratic in vertex form.
y=a(x-h)^2+k

a is the vertical stretch. If it is big, there is a lot of stretch. If it it less than 1, there is compression.

h is the horizontal shift. Notice the "-" in the equation.
This means a h-value of +4 as seen in the question is really a -4, shifting the graph left.

k is the vertical shift. It moves the graph up/down. Positive k moves the graph up while negative k move the graph down. Simple.

Now the graphs. I do one transformation each time to show the steps.

y=x^2
graph{x^2 [-4.75, 5.25, -0.98, 4.02]}

y=2x^2
graph{2x^2 [-4.75, 5.25, -0.98, 4.02]}

y=2(x+4)^2
graph{2(x+4)^2 [-8.25, 1.75, -0.9, 4.1]}

y=2(x+4)^2-3
graph{2(x+4)^2-3 [-8.04, 1.96, -3.22, 1.78]}