Question

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

Answer 1

Answer:

A and B

Step-by-step explanation:

We are given that

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

$g(x)=(x^2-2\times x\times 2+4)-4+3=(x-2)^2-1$

Compare with it

$y=(x-h)^2+k$

Where vertex=(h,k)

We get

Vertex of g=(2,-1)

$f(x)=x^2-4x=(x^2-2\times x\times 2+4)-4=(x-2)^2-4$

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

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

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

$x=\frac{4}{2}=2$

$f'(x)=2x-4$

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

$x=\frac{4}{2}=2$

$g''(x)=2>0$

$f''(x)=2>0$

f and g have both minima at x=2

Hence, option A and B are true.