Let the graph of g be a vertical stretch by a factor of 6 followed by a translation 2 units left of the graph of f(x)= x^2. Write a rule for g. g(x)= ?

Question

Showing work would be nice please

Answer 1

Hi Alyssa!

So when you do a translation on a quadratic function it will be in this form.

y= a(bx-c)² + d

a: vertical stretch/shrink factor

b: horizontal stretch/shrink factor of 1/b

-c: c units right

+c: c units left

+ d: d units up

-d: d units down

You have a vertical stretch of 6 and 2 units left.

a= 6

+c = +2 : 2 units left

b and d are not needed. b=1 d=0

g(x)= 6(x+2)²

I hope this information helps! Have a great day!

Mrs. S

Answer 2

when f(x) is stetched by a factor of k, the new function becomes kf(x);

when f(x) is shift by a, the new function is f(x-a). If a is positive, the function is shifted to the right and if a is negative, the function is shifted to the left.

Apply these rules to g, and we have k = 6 and a = -2,

so g(x) = 6f(x+2) = 6(x+2)^2