Translating parabola through two points?

Question

Here's the question:  "Write down the equation of the parabola y=x^2 - x - 6 translated through (2, 3) [the 2 is above the 3] 
I'm not interested in the answer so much, as I am about finding out where I can learn the method to answer these types of questions. 
If you could supply links or explain yourself how I can go about answering this question, It'll be greatly appreciated. 

Many thanks.

Dan · Accepted Answer

I'm assuming that you want to translate the parabola by a vector (2 3)

Let's call (x,y) be a point on the original parabola and (x₁,y₁) the translation of (x,y) by (2 3 )

x₁-x= 2  and x= x₁ -2
y₁-y= 3 and y=y₁ - 3

Now just substitute x= x₁ -2 and y=y₁ - 3 in the original equation
Therefore the equation of the translated parabola is: 

y₁ - 3 = (x₁ -2)² - (x₁ -2) - 6
y₁ = x₁²  - 5x₁ + 3

Now if you want to check the answer just consider a point on the original parabola (e.g (1, -6)) and just add the vector (2 3) and you get the point (3, -3) which is on the second parabola:
-3 = 3² - 5(3) +3 = 9 -15 +3 = -3

husted · Answer

Take 3 aspects to your parabola, for each and every compute a factor one million.0cm out from it following a line perpendicular to the wall. You can compute the perpendicular traces with realistic calculus the get the slope and algebra to get the tangent. Solve y=ax^two + bx + c that intersects the 3 new aspects you could have computed.

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Translating parabola through two points?

2 Answers