# How do you find the vertex of #y= -x^2+4x-3#?

##### 1 Answer

Apr 9, 2016

(2 , 1)

#### Explanation:

The standard form of a quadratic function is :

#color(red)(|bar(ul(color(white)(a/a)color(black)(y=ax^2 + bx + c)color(white)(a/a)|)))# The function here : y

#= - x^2 + 4x - 3 " is in this form " # with a = -1 , b = 4 and c = -3

x-coord of vertex =

# color(blue)(|bar(ul(color(white)(a/a)color(black)((-b)/(2a)color(white)(a/a)|))) #

#rArr x_(vertex) = (-4)/(-2) = 2 # To find corresponding value of y-coord of vertex , substitute

x = 2 into the function.x = 2 : y

# = -(2)^2 + 4(2) - 3 = -4+ 8 -3 = 1#

#rArr vertex = color(orange)(|bar(ul(color(white)(a/a)color(black)( 2 , 1 )color(white)(a/a)|)))# Here is the graph of y#= -x^2+4x-3

graph{-x^2+4x-3 [-10, 10, -5, 5]}