Question

The function f(x) = x2. The graph of g(x) is f(x) translated to the left 6 units and down 5 units. What is the function rule for g(x)?
A. g(x) = (x + 6)2 - 5
B. g(x) = (x - 5)2 + 6
C. g(x) = (x - 6)2 + 5
D. g(x) = (x + 5)2 - 6

Answer 1

A

Answer 2

So a parabola has the generic formula:
\[y=(x-h)^{2} + k\]
where (h,k) is the bottom/top of the parabola

Answer 3

So what is the bottom/top of the parabola of
\[y=x^{2}\]

Answer 4

How do you know it's a?

Answer 5

Take a look at what I posted above. I'll walk you through it!

Answer 6

Okay okay :) Okay so...what next?

Answer 7

The easiest way to figure out the new graph is to figure out how the bottom/top of the graph moved. So we have
\[y = x^{2} \]
what would be the coordinate of the bottom/top?

Answer 8

y= -x^2?

Answer 9

I'm just looking for an (x,y) coordinate. So the generic formula for a parabola is
\[y = (x-h)^{2} + k\]
where (h,k) is the coordinate of the bottom/top of the parabola. So now we have
\[y = x^{2}\]
which is the same as
\[y=(x-0)^{2} + 0\]
so what is the (x,y) coordinate of the bottom/top?

Answer 10

im so confused /.\

Answer 11

Okay, which part is confusing?

Answer 12

( h,k) ?

Answer 13

So (h,k) is called the vertex of the parabola, which is like the bottom of the dip in a graph.

The circled part in the graph is the vertex.