3.) Which statements are true about the graph of the function f(x) = 6x – 4 + x2? Check all that apply.

The vertex form of the function is f(x) = (x – 2)2 + 2.

The vertex of the function is (–3, –13).

The axis of symmetry for the function is x = 3.

The graph increases over the interval (–3, infinity symbol).

The function does not cross the x-axis.

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frika frika · Answer 1 · 2018-08-23T10:52:16-04:00

Find the vertex of the parabola given by the formula \(f(x) = 6x - 4 + x^2\):

\(f(x) = 6x - 4 + x^2=x^2+2\cdot x\cdot 3-4=x^2+2\cdot x\cdot 3+3^2-3^2-4=(x+3)^2-9-4=(x+3)^2-13.\)

1. As you can see this vertex form differ from the vertex form in option A, then A is incorrect.

2. When x=-3, f(-3)=-13 and the vertex has coordinates (-3,-13) - option B is true.

3. From the attached graph you can see that the axe of symmetry is line x=-3 that passes through the vertex. This means that choice C is incorrect.

4. From the attached graph you can see that the function is increasing for x>-3 and decreasing for x<-3. Option D is correct.

5. The graph intersects x-axis at two points (see attached diagram). Option E is incorrect.

azikennamdi azikennamdi · Answer 2 · 2022-04-05T09:03:07-04:00

It is clear from the information given that Both Options B and Option D are correct. While options A and C are incorrect.

The set of all points in the plane of the form (x, f(x)) is known as the graph of a function f(x).

In order words, it is the collection of all ordered pairs of the function. Examples of real-life applications of Graph Functions are:

Learn more about the Graph of a Function at:

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