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lara [203]
4 years ago
15

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

Mathematics
1 answer:
Tanya [424]4 years ago
8 0

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.

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