What is the vertex of # y= -3x^2-x-2(3x+5)^2#?

Question

What is the vertex of #  y= -3x^2-x-2(3x+5)^2#?

Eva Adamson · Accepted Answer

The vertex is at #(- 61/42, - 10059/1764)# or #(-1.45,-5.70)#

You can find the vertex from ANY of the three forms of a parabola: Standard, factored and vertex. Since it is simpler I'm going to converted this into standard form.

#y= -3x^2-x-2(3x+5)^2#

#y= -3x^2-x-2*(9x^2+2*5*3*x+25) # #y= -3x^2-x-18x^2-60x-50 # #y= -21x^2-61x-50 #

# x_{vertex} = {-b}/{2a}=61 /{2*(-21)}=- 61/42~= -1.45 #

(you can prove this by either completing the square in general or averaging the roots found from the quadratic equation)

and then substituted it back into the expression to find #y_{vertex}#

#y_{vertex}= -21*(-61/42)^2-61*(-61/42)-50 #

#y_{vertex}={-21*61*61}/{42*42}+{61*61*42}/{42*42} - {50*42*42}/{42*42}#

#y_{vertex}={ -21*61*61+61*61*42 - 50*42*42}/{42*42}#

#y_{vertex}=-10059/1764~=-5.70#

The vertex is at #(- 61/42, - 10059/1764)# or #(-1.45,-5.70)#

Avery Alexander · Answer

undefined The vertex of the quadratic function y = -3x^2 - x - 2(3x + 5)^2 is (-5/3, -49/3).

Jace Anderson · Answer

undefined To find the vertex of the quadratic function $ y = -3x^2 - x - 2(3x + 5)^2 $, first, rewrite the equation in standard form $ y = ax^2 + bx + c $. Then, identify the values of $ a $, $ b $, and $ c $. Once you have these values, the x-coordinate of the vertex can be found using the formula $ x = -\frac{b}{2a} $. Finally, substitute the x-coordinate into the original equation to find the corresponding y-coordinate.