Question

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

Answer 1

(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]}