Question
The vertex of a parabola is at (-2,4), and the x-intercepts are at -6 and 2. Determine the domain and range of the function.
a.
D: all real numbers
R: all real numbers
b.
D: all real numbers
R: y ≤ 4
c.
D: -6 ≤ x ≤ 2
R: y ≤ 4
d.
D: x ≤ 4
R: all real numbers
a.
D: all real numbers
R: all real numbers
b.
D: all real numbers
R: y ≤ 4
c.
D: -6 ≤ x ≤ 2
R: y ≤ 4
d.
D: x ≤ 4
R: all real numbers
Answers
Steve
domain is all reals for all polynomials. So, C and D are out.
since a parabola has a vertex, it has a maximum or a minimum, so the range cannot be all reals. So, A is out.
B must be the answer.
The only confusion might be whether the vertex is a max or a min. If B is correct, it must be a maximum.
Since there are real roots, the vertex at (-2,4), which is above the x-axis, must be a maximum, so y <= 4.
since a parabola has a vertex, it has a maximum or a minimum, so the range cannot be all reals. So, A is out.
B must be the answer.
The only confusion might be whether the vertex is a max or a min. If B is correct, it must be a maximum.
Since there are real roots, the vertex at (-2,4), which is above the x-axis, must be a maximum, so y <= 4.