Question

if f(x) has a left shift of 2 units, a up shift of 3 and a vertical stretch of 4, what is the equation for f(x)?
f(x)=4(x - 2)^2 + 3
f(x)=2(x - 4)^2 + 3
f(x)=3(x + 2)^2 + 4
f(x)=4(x + 2)^2 + 3

Explanation:

Step1: Define parent function

Let parent function be $g(x)=x^2$.

Step2: Apply vertical stretch by 4

Multiply by 4: $4g(x)=4x^2$

Step3: Apply left shift of 2 units

Replace $x$ with $x+2$: $4(x+2)^2$

Step4: Apply up shift of 3 units

Add 3 to the function: $4(x+2)^2 + 3$

Answer:

$f(x)=4(x+2)^2+3$