Question

Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check a

that apply.
O p(x)=14(x + 7)²+1
O g(x) = -5(x+10)²-1
D s(x) = −(x−1)2 +0.5
O g(x)=2x² +10x-35
Ot(x)=-2x² - 4x-3

Answer 1

Two functions that have a maximum and are transformed to the left and down of the parent function f(x) = x^2 are p(x) = 14(x + 7)^2 + 1 and g(x) = -5(x + 10)^2 - 1.

Step-by-step explanation:

The parent function, f(x) = x2, has a maximum at the point (0, 0). To transform the parent function to the left and down, we need to make changes to the equation that shift the graph horizontally (to the left) and vertically (downward). Let's analyze the given options:

1. Option (a): p(x) = 14(x + 7)2 + 1 - This function is transformed to the left by 7 units and downward by 1 unit compared to the parent function. It has a maximum at the point (-7, 1). So, this option applies.
2. Option (b): g(x) = -5(x + 10)2 - 1 - This function is transformed to the left by 10 units and downward by 1 unit compared to the parent function. It has a maximum at the point (-10, -1). So, this option applies.
3. Option (c): s(x) = -(x - 1)2 + 0.5 - This function is transformed to the right by 1 unit, not to the left. So, this option does not apply.
4. Option (d): g(x) = 2x2 + 10x - 35 - This function is not transformed to the left compared to the parent function. So, this option does not apply.
5. Option (e): t(x) = -2x2 - 4x - 3 - This function is transformed to the left compared to the parent function. However, it does not have a maximum. It has a minimum at the point (-1, -5). So, this option does not apply.

Therefore, the options that apply are (a) p(x) = 14(x + 7)2 + 1 and (b) g(x) = -5(x + 10)2 - 1.