Question

2.7 independent practice & hw

1. describe each transformation as it relates to the graph of the parent function. then, sketch its graph in relation to the parent function provided.

a. $y = x^2 + 2$
transformation(s):
graph of parabola with vertex at (0,0)

b. $y = (x - 3)^2$
transformation(s):
graph of parabola with vertex at (0,0)

d. $h(x) = (x + 1)^2 - 4$
transformation(s):
graph of parabola with vertex at (0,0)

e. $h(x) = (x - 2)^2 + 3$
transformation(s):
graph of parabola with vertex at (0,0)

g. $f(x) = - (x + 4)^2 + 1$
transformation(s):
graph of parabola with vertex at (0,0)

h. $y = - (x - 1)^2 - 2$
transformation(s):
graph of parabola with vertex at (0,0)

1. use the graph of each transformed parent function to describe the transformation and write its equation.

a.
graph of parabola with vertex below origin
transformation(s):
$f(x) = $

b.
graph of parabola with vertex below origin, opening upwards
transformation(s):
$f(x) = $

c.
graph of parabola with vertex at (0,4), opening upwards, then a different parabola?
transformation(s):
$f(x) = $

d.
graph of parabola opening downwards
transformation(s):
$f(x) = $

Explanation:

Answer:

Vertical translation \(2\) units up
Horizontal translation \(3\) units right
Horizontal translation \(1\) unit left, vertical translation \(4\) units down
Horizontal translation \(2\) units right, vertical translation \(3\) units up
Reflection over the \(x\) - axis, horizontal translation \(4\) units left, vertical translation \(1\) unit up
Reflection over the \(x\) - axis, horizontal translation \(1\) unit right, vertical translation \(2\) units down