Question

ntit fl Kuta Software - Infinite Algebra 2 Vertex Form of Parabolas Use the information provided to write the vertex form equation of each parabola. 2) y=x² - 2x-5

Answer 1

We have

$y=x^2-2x-5$

where

a=1

b=-2

c=-5

First we need to find the vertex, with the next formula we will find the x-coordinate of the vertex.

$x=\frac{-b}{2a}$

we substitute the values

$\begin{gathered} x=\frac{-(-2)}{2(1)} \\ x=\frac{2}{2} \\ x=1 \end{gathered}$

then we substitute the value of the x-coordinate in the original equation in order to find the y-coordinate

$\begin{gathered} y=1^{2}-2(1)-5 \\ y=1-2-5 \\ y=-6 \end{gathered}$

the coordinates of the vertex is (1,-6)

the vertex form of the parabola is

$y=a\mleft(x-h\mright)^2+k$

where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex, the vertex form of this parabola is

$y=(x-1)^2-6$