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Which statements about functions g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are true? Select all that apply.

A. The vertex of the graph of function g is above the vertex of the graph of function f.
B. The graphs have the same axis of symmetry.
c. Function f has a maximum value and function g has a minimum value.​

2 Answers

6 votes

Answer:

The answer is B!

Explanation:

Plato answer

User Azeame
by
3.7k points
2 votes

Answer:

A and B

Explanation:

We are given that


g(x)=x^2-4x+3


g(x)=(x^2-2* x* 2+4)-4+3=(x-2)^2-1

Compare with it


y=(x-h)^2+k

Where vertex=(h,k)

We get

Vertex of g=(2,-1)


f(x)=x^2-4x=(x^2-2* x* 2+4)-4=(x-2)^2-4

Vertex of f=(2,-4)

Equation of axis of symmetry=x-coordinate of vertex

Axis of symmetry of g

x=2

Axis of symmetry of f

x=2

Differentiate w.r.t x


g'(x)=2x-4=0


2x-4=0\implies 2x=4


x=(4)/(2)=2


f'(x)=2x-4


2x-4=0\implies 2x=4


x=(4)/(2)=2


g''(x)=2>0


f''(x)=2>0

f and g have both minima at x=2

Hence, option A and B are true.

Which statements about functions g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are true? Select-example-1
User Potashin
by
3.6k points