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)

A

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

The x-coordinate of the vertex is

= -

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

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

= - =

Substitute this value into the equation for y-coordinate

y = - 3 ()² + 2 ( ) - 7

  = - + - = -

vertex = ( , - ) → A

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

b

step-by-step explanation: