Which statements are true about the graph of the function f(x) = 6x – 4 + x2? 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, ). the function does not cross the x-axis.

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

Step-by-step explanation:

The graph is shown below. From the graph you can see, the vertex is (-3,-13).

Option 2,4 are true statement.

Step-by-step explanation:

Given : Function

To find : Which statements are true about the graph of the function?

Solution :

First we have to convert the quadratic function  into vertex form where (h,k) are the vertex.

Function

Applying completing the square i.e. add and subtract half square of b,

Option 1 is incorrect.

On comparing with vertex form,

h=-3 and k=-13

So, The vertex of the function is (h,k)=(-3,-13).

Option 2 is correct.

Axis of symmetry is

Substitute a=1 and b=6

Option 3 is incorrect.

Now, We plot the graph of the function.

Refer the attached figure below.

The graph increases over the interval (–3,-13).

Option 4 is correct.

From the graph we see that it crosses x-axis.

Option 5 is incorrect.

Therefore, Option 2,4 are true statement.

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step-by-step explanation: