you have to rewrite this equation: 2(y^2)-x-4y+5=0
at first i thought it could be rewritten into a parabola or hyperbola but now i dont know. thanks for the help!
at first i thought it could be rewritten into a parabola or hyperbola but now i dont know. thanks for the help!
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2y² - x - 4y + 5 = 0
There is a only one squared variable, so it is a parabola.
The squared variable is y², not x², so the parabola is horizontal.
Put equation into vertex form for horizontal parabola:
x = a(y−k)² + h
Regroup terms
x = 2y² - 4y + 5
Factor out the leading coefficient
x = 2(y² - 2y) + 5
Complete the square
x = 2(y² - 2y + (-1)²) + 5 - 2(-1)²
x = 2(y - 1)² + 3
This is the equation of a right-opening parabola.
There is a only one squared variable, so it is a parabola.
The squared variable is y², not x², so the parabola is horizontal.
Put equation into vertex form for horizontal parabola:
x = a(y−k)² + h
Regroup terms
x = 2y² - 4y + 5
Factor out the leading coefficient
x = 2(y² - 2y) + 5
Complete the square
x = 2(y² - 2y + (-1)²) + 5 - 2(-1)²
x = 2(y - 1)² + 3
This is the equation of a right-opening parabola.