Question

Where does the graph of `y = 3x^2 − 10x − 8` cross the x-axis?

Answer 1

`x=-2/3,x=4`

Explanation:

`"to find where the graph crosses the x-axis set y = 0"`

`3x^2-10x-8=0`

`"using the a-c method to factor the quadratic"`

`"the factors of the product "3xx-8=-24`

`"which sum to - 10 are - 12 and + 2"`

`"split the middle term using these factors"`

`3x^2-12x+2x-8=0larrcolor(blue)"factor by grouping"`

`color(red)(3x)(x-4)color(red)(+2)(x-4)=0`

`"take out the "color(blue)"common factor "(x-4)`

`(x-4)(color(red)(3x+2))=0`

`"equate each factor to zero and solve for x"`

`x-4=0rArrx=4`

`3x+2=0rArrx=-2/3`
graph{3x^2-10x-8 [-10, 10, -5, 5]}