Question

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

A. (1/3, -20/3)
B. (-1/3, -20/3)
C. (-1/3, -19/3)
D. (1/3, -19/3)

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)` = -
`(b)/(2a)`

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

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

`x_(vertex)` = -
`(2)/(-6)` =
`(1)/(3)`

Substitute this value into the equation for y-coordinate

y = - 3 (
`(1)/(3)`)² + 2 (
`(1)/(3)`) - 7

= -
`(1)/(3)` +
`(2)/(3)` -
`(21)/(3)` = -
`(20)/(3)`

vertex = (
`(1)/(3)`, -
`(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