What is the the vertex of #y =3x^2+4x-18 #?

Question

Genesis Allen · Accepted Answer

#x_("vertex")=-2/3" "#I will let the reader find #""y_("vertex")#

Given:#" "y=3x^2+4x-18" "#..................................(1)

Write as:#" "y=3(x^2+4/3x)-18#

Using the #+4/3" from "(x^2+4/3x)#

#(-1/2)xx4/3 =-4/6=-2/3#

#color(blue)(x_("vertex") = -2/3)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#-2/3" " =" " -0.6666bar6" "=" "-0.6667# to 4 decimal places

#color(brown)("All you have to do now is substitute "x=-2/3" into")##color(brown)("equation (1) to find "y_("vertex"))#

Savannah Anderson · Answer

May be done as follows

The given equation is #y=3x^2+4x-18# #=>y=3[x^2+2x(2/3)+(2/3)^2-(2/3)^2 -6]# #=>y=3[(x+2/3)^2-(2/3)^2 -6]# #=>y=3[(x+2/3)^2-4/9- 6]# #=>y=3[(x+2/3)^2-58/9 ]# #=>y=3(x+2/3)^2-58/9*3 # #=>y+58/3=3(x+2/3)^2 # putting ,#y+58/3=Y and x+2/3=X # we have new equation #Y =3X^2#,which has coordinate of vertex (0,0) So putting X=0 and Y=0 in the above relation we get #x=-2/3# and #y=-58/3 =-19 1/3# so the actual coordinate of vertex is # (-2/3,-19 1/3)#

Eva Adamson · Answer

undefined The vertex of the quadratic function y = 3x^2 + 4x - 18 is calculated using the formula x = -b / (2a), where a = 3 and b = 4. Plugging in the values, we get x = -4 / (2 * 3) = -4 / 6 = -2/3. To find the corresponding y-coordinate, plug x = -2/3 into the equation. Therefore, the vertex is (-2/3, y), where y = 3(-2/3)^2 + 4(-2/3) - 18. Calculate y to find the exact coordinates of the vertex.