Question

Write 2 quadratic equations (of any form) that are not equivalent, each with a vertex of (4,5).

Answer 1

y = (x-4)²+5

y = -
`(1)/(2)` (x-4)²+5

Explanation:

Normally, you are given a function and there are certain transformations you can do to move said function around.

I would suggest graphing these out on a calculator or desmos graphing to see what I'm talking about

Given y=x² normally results in a parabola with a vertex at (0,0)

You can shift this function up by adding 5 to it.

y = x² + 5 would make the vertex (0,5)

Then, you can move the function left by adding a number to the function or to the right by subtracting a number, as shown below:

y = (x-4)² + 5 means that the vertex of the graph is now UP 5 and RIGHT 4

With this info, you can add any constant in front of the parentheses and it will not affect the location of the vertex, for example:

30000(x-4)² + 5 does not move the vertex and neither will

.01(x-4)²+5

I hope this helps explain transformations a bit. I would again recommend graphing these out for yourself to see what I'm talking about