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Can someone please help me

Can someone please help me-example-1

1 Answer

5 votes

Answer:

Vertex form:
y=(1)/(2)(x-2)^2-3

Standard Form:
y=0.50x^2-2x-1

Explanation:

Well the vertex form of an equation is given in the form:
y=a(x-h)^2+k where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you:
y=a(x-2)^2-3. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in

Plug in (0, -1) as (x, y)


-1 = a(0-2)^2-3

calculate inside the parenthesis


-1 = a(-2)^2-3

square the -2


-1 = 4a-3

Add 3 to both 3 to both sides


2 = 4a

divide both sides by 4


a=(1)/(2)

This gives you the equation:
y=(1)/(2)(x-2)^2-3

To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to:
(a+b)^2=a^2+2ab+b^2.

Original equation:


y=(1)/(2)(x-2)^2-3

expand square binomial:


y=(1)/(2)(x^2-4x+4)^2-3

Distribute the 1/2


y=0.50x^2-2x+2-3

Combine like terms:


y=0.50x^2-2x-1

User Gpoo
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