Translating parabola through two points?
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.
Answers & Comments
Verified 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
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.