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I need help on my mathhhhhh

I need help on my mathhhhhh-example-1

1 Answer

2 votes

Answer:

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

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