How do you find the vertex and axis of symmetry of #y = 3x^2 + 7x – 4#?

1 Answer
Mar 7, 2016

#color(blue)(x_("vertex")=-7/6)#
#color(blue)("Axis of symmetry "-> x=-7/6#
I will let you solve for #y_("vertex")# by substitution

Explanation:

Given:#" "y=3x^2+7x-4#

Write as:#" " y=3(x^2+7/3x)-4#

Consider the #7/3" from "7/3x#

Apply: #" "(-1/2)xx7/3 = -7/6#

#color(blue)(x_("vertex")=-7/6)#

#color(blue)("Axis of symmetry "-> x=-7/6#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute #color(red)(x=-7/6)# in the original equation to find #y_("vertex")#

#y_("vertex") = 3(color(red)(-7/6))^2 +7(color(red)(-7/6))-4#

I will let you finish this bit