Question

Q1 :Let f(x)=2x^2−8

The quadratic function g(x) is f(x) translated 2 units down


What is the equation for g(x)


Q2 Let f(x)=
`(3)/(4)`x2−1.


The function g(x) is a vertical stretch of f(x) by a factor of 8.


What is the equation of g(x)?


Q3 The graph of the function g(x) is a transformation of the parent function f(x)=x2 .


Which equation describes the function g?

(refer to picture attached)

A. g(x)=x2+2 ​

B. g(x)=(x−2)2

C. g(x)=(x+2)2 ​

D. g(x)=x2−2

Answer 1

Question # 1.


`f(x) = 2 x^(2) -8 \\`
g(x) is the translation of f(x) 2 units down.

Vertical translation can be expressed as addition or subtraction of a number from the function value. Subtraction indicates that the function is translated down. So, translation of f(x) by 2 units down can be expressed as:

g(x) = f(x) - 2
Using the value of f(x), we can write:


`g(x)= 2x^(2) -8-2 \\ \\ g(x)=2 x^(2) -10`

Question # 2


`f(x)= (3)/(4) x^(2) -1`

A function can be vertically stretched by multiplying it with a number having magnitude greater than 1. f(x) is to be stretched by a factor of 8 to get g(x), so we can write:

g(x) = 8 * f(x)

Using the value of f(x) we can write:


`g(x)=8* ((3)/(4) x^(2) -1) \\ \\ g(x)=6 x^(2) -8`