Question

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

Answer 1

Complete question is;

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.

Answer:

Options A & B are correct

Step-by-step explanation:

I've drawn and attached a graph showing the functions f(x) and g(x).

The function f(x) is depicted by the blue curve while the function g(x) is depicted by the red curve.

Now, from the graph attached, we see that the vertex which is the highest point of the graph is;

for f(x); (2, -4)

For g(x); (2, -1)

Thus,the vertex of the function g is see to be higher than that of f from the graph. So option A is correct.

Axis of symmetry is a vertical line that divides the parabola of a graph into 2 congruent parts. This means it is a vertical line that passes through the vertex.

From the graph, we can see both of their vertex have their x value as 2. Thus, their axis of symmetry are the same.

So option B is also correct.

The function will have a maximum value if the y-value at that point is larger than all other y-values while it's a minimum value if the y-value at that point is lesser than all other y-values on the graph.

In the attached graph, both parabola have a minimum value as they both have a lowest y-value.

Thus, option C is not correct.