Given f(x)=x2−3x−4 and g(x)=|x+3|−2 , which value is a solution to the equation f(x)=g(x) ? A
−4

B
−3

C
−1

D
4

The correct options are 1 and 4.

Step-by-step explanation:

The given function is

Add and subtract in the parentheses

....(1)

The vertex form of the parabola is  . Option 2 is incorrect.

The general vertex form of a parabola is

....(2)

Where, (h,k) is the vertex of the parabola.

On comparing (1) and (2) we get

Therefore the vertex of the function is (-10,-117).  Option 1 is correct.

It is upward parabola, so the minimum value of the function is -117. Option 3 is incorrect.

The vertex of the function f(x)=x² is (0,0) and the vertex of h(x) is (-10,-117).

It means the f(x) shifts left by 10 units and down 117 units. Option 4 is correct.

The axis of symmetry of the function is x=h.

So, the axis of symmetry is

Therefore option is x=-10. Option 5 is incorrect.