Question

Can someone explain this please

What will the point (-3, 9) from the base parabola, be transformed to after:
A vertical stretch by a factor of 2:
Followed by a vertical reflection:
Followed by a horizontal translation of 4 units to the right:
Followed by a vertical translation of 2 units up:

What will the equation be?

Answer 1

This is quadratics

Answer 2

So we start with the function, the base parabola, \(\large y=x^2\)

Stretching it by a factor of 2, \(\large y=2x^2\)

Then reflecting it vertically, \(\large y=-2x^2\)

Then a horizontal shift to the RIGHT 4 units, \(\large y=-2(x-4)^2\)

Then finally, a vertical shift UP 2 units, \(\large y=-2(x-4)^2+2\)

Answer 3

but the question says what will the point (-3,9) be ?

Answer 4

So there is the equation. Let's see if we can figure out where (-3,9) moves to.. hmm :\

Answer 5

Is the question asking us to make an equation using the points -3, 9 or without the points

Answer 6

The last part says "What will the equation be?"
That's the part we've determined already.
It doesn't involve the point (-3,9).


I'm not exactly sure how they want us to do that first part.
It seems the question wants to know where that point would be on our new parabola, relative to it's location on the old one.

We've stretched it, and moved things around .. I'm not sure how we would determine that :O

Hmm

Answer 7

I guess we could measure from 3 units left of the vertex of our new parabola,
and determine the function value it gives us.

\(\large f(x)=-2(x-4)^2+2\)

Our function has a vertex at \(\large (4,2)\).
So three units left of that would be at x=1.

\(\large f(1)=-2(1-4)^2+2\)
And this should tell us where that point now lies. I think...

Answer 8

Hmm kinda confusing though XD maybe there's a simpler way to do that.

Answer 9

Thats fine Ill check with my teacher