Select all the statements about functions g(x) = x2 − 4x + 3 and f(x) = x2 − 4x that are true. A. The vertex of the graph of fun

Question

3 years ago

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Select all the statements about functions g(x) = x2 − 4x + 3 and f(x) = x2 − 4x that are true. A. The vertex of the graph of fun

ction 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. D. The graphs never intersect. E. The graphs have the same y-intercept.

Mathematics

2 answers:

Verizon [17] · Answer 1 · 2022-05-25T08:58:17+03:00

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Answer:

A, B, D

Step-by-step explanation:

We observe that g(x) = f(x) +3, which means it is the graph of f(x) translated up 3 units. That translation does not change the axis of symmetry, but it puts the vertex of g above the vertex of f (by 3 units).

Since each point on the graph of g is 3 units above the corresponding point of f, the graphs cannot intersect.

The true statements are ...

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.

D. The graphs never intersect.