Question

if you apply the changes below to the quadratic parent function, f(x)=x^2, which of these is the equation of the new function

Answer 1

Answer:

Option: B is the correct answer

                  B.     $g(x)=-5(x+1)^2$

Step-by-step explanation:

We are given a parent function f(x) as:

$f(x)=x^2$

We know that when a function is shifted k units to the left then the transformation is given by:

              f(x) →f(x+k)

and when a function is vertically stretched  by a factor of a then the transformation is given by:

             f(x) → a f(x)

and when the reflection of function f(x) is done over the x-axis then the rule of transformation is:

                        f(x) →  -f(x)

Hence, we will go through the transformation one by one

• Shift of one unit left

              This means that:

         f(x) → f(x+1)

• Vertically stretch by a factor of 5.

               This means that:

                 f(x+1) → 5 f(x+1)

• and lastly reflect over the x-axis

       Hence, we get transformation as:

              5 f(x+1) → -5f(x+1)

          Hence, we get the resultant function as:

              $g(x)=-5(x+1)^2$

Answer 2

Answer:

the answer will be B