Question

The graph represents the function f(x) = x2 + 3x + 2.

If g(x) is the reflection of f(x) across the x-axis, g(x) = .

(Write the function in standard form. Use ^ to indicate an exponent.)

Answer 1

Answer: The standard form of g(x) is
`g(x)=-x^2-3x-2.`

Step-by-step explanation: The graph in the figure represents the following function :

`f(x)=x^2+3x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

Given that g(x) is the reflection of f(x) across the X-axis.

We are to find the expression for the function g(x).

We know that

a reflection X-axis will change the sign before the y-co-ordinate of the equation.

So, in equation (i), we get

`f(x)=x^2+3x+2\\\\\Rightarrow -f(x)=-x^2-3x-2\\\\\Rightarrow g(x)=-x^2-3x-2.`

Thus, the standard form of g(x) is
`g(x)=-x^2-3x-2.`

The graph of f(x) compared to g(x) is shown in the attached figure below.

Answer 2

Refrection across the x-axis changes the sign of the function (i.e. y)
Therefore, g(x) = -f(x) = -(x^2 + 3x + 2) = -x^2 - 3x - 2
g(x) = -x^2 - 3x - 2