Question

Drag the tiles to the correct boxes to complete the pairs.

Match the graphs with the functions they represent.

Answer 1

The parent function for a concave up parabola with its vertex at the origin is

y=a(x-h)^2+k.

+a points the parabola concave up

-a points the parabola concave down

h moves the vertex along the x axis that many times

k moves the vertex along the y axis that many times.

if you need more clarification comment on this question.

Answer 2

The required functions are
`f(x)=x^2+3`,
`g(x)=2x^2-3`,
`h(x)=x^2-3` and
`j(x)=-2x^2-3`.

Explanation:

The vertex from of a parabola is

`y=a(x-h)^2+k`

Where, (h,k) is the vertex of parabola is a is the vertical stretch factor.

If a is negative, then it is downward parabola and if a is positive then it is an upward parabola.

If |a|<1, then it is compressed vertical and if |a|>1, then it is stretched vertically.

The graph of f(x) has vertex at (0,3) and it is not stretch vertically so the value of a is 1. So, the function f(x) is defined as

`f(x)=1(x-0)^2+3`

`f(x)=x^2+3`

The graph of g(x) has vertex at (0,-3) and it is stretch vertically by factor 2 so the value of a is 2. So, the function g(x) is defined as

`g(x)=2(x-0)^2-3`

`g(x)=2x^2-3`

The graph of h(x) has vertex at (0,-3) and it is not stretch vertically so the value of a is 1. So, the function h(x) is defined as

`h(x)=1(x-0)^2-3`

`h(x)=x^2-3`

The graph of j(x) has vertex at (0,-3) and it is stretch vertically by factor 2 and it is downward so the value of a is -2. So, the function j(x) is defined as

`j(x)=-2(x-0)^2-3`

`j(x)=-2x^2-3`

Therefore the required functions are
`f(x)=x^2+3`,
`g(x)=2x^2-3`,
`h(x)=x^2-3` and
`j(x)=-2x^2-3`.