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=(-b)/(2a)`

we substitute the values

`\begin{gathered} x=(-(-2))/(2(1)) \\ x=(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`