Question

Quadratic functions q and w are graphed on the same coordinate grid. The vertex of the graph of q is 18 units below the vertex of the graph of w. Which pair of functions could have been used to create the graphs of q and w?

A. q(x)=18
`x^(2)` and w(x)=
`x^(2)`


B. q(x)=
`x^(2)` +18 and w(x)=
`x^(2)`


C. q(x)=-18
`x^(2)` and w(x)=
`x^(2)`


D. q(x)=
`x^(2)`-18 and w(x)=
`x^(2)`


Thank you in advance for any help!

Answer 1

You’re answer is most likely A

Answer 2

The only pair of quadratic functions whose graphs satisfy the condition are q(x) =
`x^(2)` - 18 and w(x) =
`x^(2)` and the correct option is D.

Since the vertex of the graph of q is 18 units below the vertex of the graph of w, this means that the y-value of q(x) is always 18 less than the y-value of w(x) for any given x-value.

Option A, q(x) = 18
`x^(2)` and w(x) =
`x^(2)`, does not satisfy this condition because the difference in their y-values is not always 18.

Option B, q(x) =
`x^(2)` + 18 and w(x) =
`x^(2)`, also does not satisfy the condition because the difference in their y-values is always 18, which means their graphs would coincide.

Option C, q(x) = -18
`x^(2)` and w(x) =
`x^(2)`, does not satisfy the condition because the vertex of the graph of q would be 18 units above the vertex of the graph of w, not 18 units below.

Option D, q(x) =
`x^(2)` - 18 and w(x) =
`x^(2)`, satisfies the condition because the difference in their y-values is always 18. This means that the vertex of the graph of q is 18 units below the vertex of the graph of w.

Therefore, the pair of functions that could have been used to create the graphs of q and w is q(x) =
`x^(2)` - 18 and w(x) =
`x^(2)` and the correct option is D.