Question

Can i have some super quick help? subject is stretching and reflecting quadratic functions

Answer 1

#1

Passes through

• (-1,4)

y=x² passes through (-1,1)

Stepped 4 times

• y=4x²

#2

First make a negative as parabola is opening downwards.

• y=-x²

Passes through (1,-2)

y=-x² passes through (1,-1)

So

final graph

• y=-2x²

Answer 2

a) Stretched parallel to the y-axis by a scale factor of 5

b) Stretched parallel to the y-axis by a scale factor of 5/2 and reflected in the x-axis.

Explanation:

Transformation

y = a f(x)

• The graph of a f(x) is f(x) stretched parallel to the y-axis (vertically) by a factor of a.
• If a < 0, the graph is also reflected in the x-axis

Part (a)

`\textsf{Parent function}:\quad y=x^2`

`\textsf{Transformed function}:\quad y=5x^2`

Transformation: Stretched parallel to the y-axis by a scale factor of 5.

Part (b)

`\textsf{Parent function}:\quad y=x^2`

`\textsf{Transformed function}:\quad y=-(5)/(2)x^2`

Stretched parallel to the y-axis by a scale factor of 5/2 and reflected in the x-axis.