Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6? O left 1 unit, up 5 units
Oright 1 unit, up 5 units
left 2 units, up 2 units
Oright 2 units, up 2 units

The translation is left 1 unit, up 5 units ⇒ A

Step-by-step explanation:

Let us revise the rules of translation of a function

The vertex form of the quadratic function is f(x) = ax² + bx + c, where a, b, and c are constant is f(x) = a(x - h)² + k, where h =  and k = f(h)

You will use the vertex form to find the translation

∵ g(x) = x² + 2x + 6

∴ a = 1 and b = 2

→ use the rule of h to find it

∴ h =

∴ h = -1

→ Use it to find k

∵ g(h) = k

∴ k = g(-1)

→ Substitute x by -1 in g to find k

∴ k = (-1)² + 2(-1) + 6 = 1 - 2 + 6

∴ k = 5

→ Substitute the values of h and k in the vertex form above

∴ g(x) = 1(x - -1)² + 5

∴ g(x) = (x + 1)² + 5

→ By using the 2nd and 3rd rules of translation above

∴ f(x) is translated 1 unit to the left and 5 units up

∴ The translation is left 1 unit, up 5 units

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!

if im not mistaking its

step-by-step explanation: