A
Given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then
The x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = - 3x² + 2x - 7 is in standard form
with a = - 3, b = 2 and c = - 7, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{-6}[/tex] = [tex]\frac{1}{3}[/tex]
Substitute this value into the equation for y-coordinate
y = - 3 ([tex]\frac{1}{3}[/tex])² + 2 ( [tex]\frac{1}{3}[/tex]) - 7
= - [tex]\frac{1}{3}[/tex] + [tex]\frac{2}{3}[/tex] - [tex]\frac{21}{3}[/tex] = - [tex]\frac{20}{3}[/tex]
vertex = ( [tex]\frac{1}{3}[/tex], - [tex]\frac{20}{3}[/tex]) → A
1) with this formula you can calculate the value of x , x = -b/2a
2) substitute the values x = -(2)/2(-3) = 2/6 = 1/3
3) substitute the value of x in the function
y= -(3)(1/3)^2+(2*1/3)-7 = -20/ 3, therefore , the correct option is A
