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Use a graphing calculator to sketch the graph of the quadratic equation, and then give the coordinates for the x-
intercepts (if they exist).
y = 6x2 - 15x + 6
a. (0.5, 0); (2,0)
c. (-0.5, 0); (-2, 0)
b. (-0.5, 0); (2,0)
d. (0.5, 0); (-2, 0)

Respuesta :

Given:

The quadratic equation is

[tex]y=6x^2-15x+6[/tex]

To find:

The x-intercepts of the given equation.

Solution:

We have,

[tex]y=6x^2-15x+6[/tex]

Splitting the middle term, we get

[tex]y=6x^2-12x-3x+6[/tex]

[tex]y=6x(x-2)-3(x-2)[/tex]

[tex]y=(x-2)(6x-3)[/tex]

For x-intercepts, y=0.

[tex](x-2)(6x-3)=0[/tex]

Using zero product property, we get

[tex]x-2=0\text{ and }6x-3=0[/tex]

[tex]x=2\text{ and }6x=3[/tex]

[tex]x=2\text{ and }x=\dfrac{3}{6}[/tex]

[tex]x=2\text{ and }x=0.5[/tex]

So, the x-intercepts are (0.5,0) and (2,0).

Therefore, the correct option is a.

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