Algebra II Help!

Question

 If the parent function f(x) = x2 is modified to g(x) = 2x2 + 1, which statement is true about g(x)?

Answer 1

The "+1" translates the function f(x) up one unit along the y axis.  All y-values will increase by 1.

 

The multiplication of "2" f(ax) where a = 2 compresses the graph horizontally by 1/2, meaning the graph parabola will become narrower.

 

f(x) = x^2 is a parabola with vertex at the origin and points (1, 1)(2,4)(4,16)

 

g(x) = 2x^2 + 1 is a parabola with a vertex at (0,1) with ordered pairs (0,1), (1,3)(2,9)(4,33).    If you graph this, the parabola is much STEEPER, meaning the new parabola will fall "inside" f(x)

Answer 2

You didn't include the statements you have to choose from but here's some facts about g(x).

 

Also, I'm assuming your f(x) = x² which isn't that clear from your question.

 

f(x) is an upward facing parabola (u-shaped) with the vertex at (0,0).

 

The "+1" in g(x) will shift the graph of f(x) upward by 1, so the vertex will be at (0,1).

The coefficient "2" in g(x) will make the parabola taller and skinnier as y will increase faster than x by a factor of 2.