Where does f(x) = 3x2 – 11x - 4 intersect the x-axis?

The x-intercepts are (4,0) and (-1/3,0).

Step-by-step explanation:

f or any relation/function will intersect the x-axis when y is 0.

Set that's what we will do is set y to 0 and solve for x.

0=3x^2-11x-4

I'm going to attempt to factor.

a=3

b=-11

c=-4

We need to find two numbers that multiply to be ac and add up to be b.

ac=-12=-12(1)

b=-11=-12+1

Let's factor 3x^2-11x-4 by grouping.

3x^2-11x-4

3x^2-12x+1x-4       ; I replaced -11x with -12x+1x

Group the first 2 pairs and group the last two pairs like so:

(3x^2-12x)+(1x-4)

Now factor what you can from each pair:

3x(x-4)+1(x-4)

Now you have two terms, both with the common factor (x-4) so factor it out:

(x-4)(3x+1)

Now let's go back to solving:

3x^2-11x-4=0

This is the same as solving:

(x-4)(3x+1)=0  (because this is just the factored form of the original equation.)

Now this means either x-4=0 or 3x+1=0.

We need to solve both.

x-4=0 can be solved by adding 4 on both sides resulting in x=4.

3x+1=0 requires two steps.

3x+1=0

Subtract 1 on both sides:

3x=-1

Divide both sides by 3:

x=-1/3

The x-intercepts are (4,0) and (-1/3,0).

The negative x-intercept is at (-1/3 , 0).

The positive x-intercept is at (4 , 0).

Explanation:

Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?

The negative x-intercept is at (-1/3 , 0).

The positive x-intercept is at (4 , 0).

Set f(x) equal to zero so

3x2 – 11x – 4 = 0

Plug in a. b, and c into the quadratic formula

and get 2 solutions:

1/3 and -4

take the opposite signs and put it in the x intercepts

the answer is

mean of samples in row 1: 8

Mean of samples in row 2:  5

Mean of samples in row 3:  6

Mean of samples in row 4:   4