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Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check
all that apply.
p(x) = 14(x + 7)² + 1

g(x) = -5(x + 10)² - 1

s(x) = –(x − 1)? +0.5

g(x) = 2x² + 10x-35

t(x) = -2x² - 4x - 3

Answer :

Using translation concepts, the functions that have a maximum and are transformed to the left and down of the parent function are given by:

  • g(x) = -5(x + 10)² - 1
  • t(x) = -2x² - 4x - 3

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

For the translations, we have that:

  • Shift left, hence x -> x + a, a > 0.
  • Shift down, hence y -> y - a, a > 0.
  • Having a maximum means that the leading coefficient is negative.

The functions that respect these conditions are:

  • g(x) = -5(x + 10)² - 1
  • t(x) = -2x² - 4x - 3 = -2(x² + 2x) - 3 = -2(x + 1)² - 1

More can be learned about translation concepts at https://brainly.com/question/4521517

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