Respuesta :

altavistard

Answer:

One point:  (2/3, 0)

Step-by-step explanation:

The fastest way to determine this is to find the discriminant, b^2-4ac:

discriminant = (-12)^2 - 4(9)(4) = 144 - 144 = 0

The rule here states that if the discriminant is 0, the function has two real, equal roots.  Those roots are

       -(-12) ± √0

x =   ---------------- = 12/18, or 2/3.

             2(9)

The graph touches the x-axis at x = 2/3, but does not cross it.  In other words, the graph intersects the x-axis at only one x value:  2/3.

x = ------------------

The graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

What is x-intercepts ?

The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of a parabola.

We have,

y = 9x² - 12x + 4

Now,

So, to get the x-intercept,

Put y = 0,

i.e.

0 = 9x² - 12x + 4

Now,

Using the mid term splitting method,

0 = 9x² - 12x + 4

0 = 9x² - 6x - 6x + 4

0 = 3x(3x - 2) -23(x - 2)

i.e.

0 = (3x - 2) (3x - 2)

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex]

And,

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex] ,

So,

The x -intercept is only at one point, i.e. [tex]x = \frac{2}{3}[/tex].

Hence, we can say that the graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

To know more about x-intercept click here

https://brainly.com/question/13054362

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