The value of b is [tex]b=3[/tex]
Explanation:
The given quadratic equation is [tex]y=3x^{2} +bx-2[/tex]
And has x - intercept [tex](-2,4)[/tex]
To determine the value of b, let us substitute the coordinates [tex](-2,4)[/tex] in the given quadratic equation [tex]y=3x^{2} +bx-2[/tex]
Substituting the x - intercept in the equation [tex]y=3x^{2} +bx-2[/tex], we have,
[tex]4=3(-2)^{2} +b(-2)-2[/tex]
Simplifying, we have,
[tex]4=3(4)-2b-2[/tex]
[tex]4=12-2b-2[/tex]
Adding the constant terms, we get,
[tex]4=10-2b[/tex]
Subtracting both sides by 10, we have,
[tex]-6=-2b[/tex]
Dividing both sides by -2, we get,
[tex]b=3[/tex]
Hence, the value of b is [tex]b=3[/tex]
