contestada

Given a quadratic function in vertex form:

f(x) = a(x - h) 2+ k

a. For what values of a does a VERTICAL STRETCH take place?

b. For what values of a does a VERTICAL COMPRESSION take
place?

c. How does a VERTICAL STRETCH compare to a HORIZONTAL
COMPRESSION?

d. For what values of a does a REFLECTION across the x-axis take
place?

Respuesta :

Answer:

See below

Step-by-step explanation:

Part A

A vertical stretch takes place when [tex]a\cdot f(x)[/tex] given that  [tex]|a| > 1[/tex]

Part B

A vertical compression takes place when [tex]a\cdot f(x)[/tex] given that [tex]0 < |a| < 1[/tex]

Part C

A vertical stretch is different than a horizontal compression:

  • In a vertical stretch, the input stays the same, but the output is multiplied by the scale factor
  • In a horizontal compression, the output stays the same, but the input is multiplied by the scale factor

Part D

A reflection across the x-axis means that the output, our y-variable, is the opposite sign. This means that all values of [tex]a[/tex] must be negative such that [tex]a\cdot f(x)[/tex] as mentioned in parts A and B. Also, in part C, since our scale factor is negative, the output is the only one being multiplied by the scale factor.

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