Equation of a Parabola Passing Through (2,-2√2) Opening to the Right

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The equation of a parabola passing through the point (2,-2√2) and opening to the right is derived using the formula y² = 4cx. By substituting the coordinates into the equation, the calculation initially led to c = 1/4, resulting in y² = x. However, the correct calculation requires squaring the entire y value, which is -2√2, leading to the correct equation y² = 4x. The error occurred in not squaring the full value of y, which should have resulted in 8 instead of 2. The final correct equation is confirmed as y² = 4x.
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Homework Statement


Write the equation of a parabola passing through the point (2,-2√2) and opening to the right.


Homework Equations


Parabola with a horizontal axis and vertex (0,0) y^2 = 4cx



The Attempt at a Solution



Since the parabola opens right I will use the equation y^2 = 4cx
I will let x = 2 and y = -2√2
y^2 = 4c(2)
(-2√2)^2 = 4c(2)
2 = 4c(2)
2 = 8c
1/4 = c
y^2 = 4(1/4)x
y^2 = x

* The answer in my student solution mannual says the correct answer should be y^2 = 4x. When I graph this, my graphs supports this answer, where did I go wrong?
 
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Sorry, I figured it out. When i squared my y value, i only squared the √2, giving me 2, instead of squaring -2√2 which would give 8.
 

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