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

Apr 9, 2016

(2 , 1)

Explanation:

The standard form of a quadratic function is :

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = a {x}^{2} + b x + c} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The function here : y $= - {x}^{2} + 4 x - 3 \text{ is in this form }$

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)|)))

$\Rightarrow {x}_{v e r t e x} = \frac{- 4}{- 2} = 2$

To find corresponding value of y-coord of vertex , substitute
x = 2 into the function.

x = 2 : y $= - {\left(2\right)}^{2} + 4 \left(2\right) - 3 = - 4 + 8 - 3 = 1$

$\Rightarrow v e r t e x = \textcolor{\mathmr{and} a n \ge}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{2 , 1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Here is the graph of y#= -x^2+4x-3
graph{-x^2+4x-3 [-10, 10, -5, 5]}