Week 12 – Pre Calc 11 – Correctly Interpreting Vertex Translation

This week in Pre Calc 11 we were learning about quadratic functions and equations and how to interpret things like the various equation forms that you can use to describe a function we also learned how to use these equations to find the 7 aspects of a parabola (vertex, line of symmetry, x intercepts, y intercepts, stretch, domain, and range) and while doing a question relating to making equations i noticed a mistake i made.

the question was asking me to write an equation based of the parent function of y=. the question had asked me to modify the equation to include a translation of 3 units left 8 units up and so I wrote +8 because i thought that since the modifier to x was negative and therefore the vertex would be in quadrant 3 at (-3,8) but actually in order to get the vertex to be at (-3,8) the equation would need to be +8 because in order for the x to go left it needs to be a positive number and the opposite for going right

here is a picture explaining it:

it is important to know how to do this as the vertex is the most important point on a parabola and plotting it incorrectly could potentially give you a parabola nowhere near the original