How do you sketch the graph of y=(x-2)^2-7 and describe the transformation?

1 Answer
Somebody N.
Sep 9, 2017

See below.

Explanation:

The function is in the form: a(x - h )^2 +k
Where h is the axis of symmetry, and k is the maximum or minimum value of the function. This is known as the vertex of the parabola.

From example: vertex is at ( 2 , -7 )

We now need to find roots and y axis intercept. This will then give us a sufficient number of plotting points.

Expand y = ( x - 2 )^2 - 7 , and equate it to 0

x^2 - 4x - 3 = 0

Solution by quadratic formula gives roots:

( 2 + sqrt7 , 0 ) and ( 2 - sqrt(7) , 0 )

y axis intercept is where x = 0

y = (0)^2 - 4(0) -3

( 0 , -3 )

So all plotting points are:

( 2 , -7 ) ,( 2 + sqrt7 , 0 ) , ( 2 - sqrt(7) , 0 ) , ( 0 , -3 )

Graph:
graph{x^2 -4x -3 [-5, 10, -12.8, 20]}

This can be viewed as the graph of y = x^2 translated 2 units to the right and 7 units in the - y direction.

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