Question

What is the vertex of the equation, y= -3x^2+2x-7?

Answer 1

A

Given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then

The x-coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

y = - 3x² + 2x - 7 is in standard form

with a = - 3, b = 2 and c = - 7, hence

$x_{vertex}$ = - $\frac{2}{-6}$ = $\frac{1}{3}$

Substitute this value into the equation for y-coordinate

y = - 3 ($\frac{1}{3}$)² + 2 ( $\frac{1}{3}$) - 7

  = - $\frac{1}{3}$ + $\frac{2}{3}$ - $\frac{21}{3}$ = - $\frac{20}{3}$

vertex = ( $\frac{1}{3}$, - $\frac{20}{3}$) → A

Answer 2

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