Question

I need help on my mathhhhhh

Answer 1

y =
`(1)/(2)` x² - 2x + 1

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (2, - 1 ) , then

y = a(x - 2)² - 1

to find a substitute any other point that lies on the graph into the equation.

using (0, 1 )

1 = a(0 - 2)² - 1 ( add 1 to both sides )

2 = a(- 2)² = 4a ( divide both sides by 4 )

`(2)/(4)` = a , that is

a =
`(1)/(2)`

y =
`(1)/(2)` (x - 2)² - 1 ← equation in vertex form

expand (x - 2)² using FOIL

y =
`(1)/(2)` (x² - 4x + 4) - 1 ← distribute parenthesis

y =
`(1)/(2)` x² - 2x + 2 - 1 ← collect like terms

y =
`(1)/(2)` x² - 2x + 1 ← in standard form