To determine which equation describes a parabola that opens left or right and whose vertex is at the point [tex]\((h, v)\)[/tex], we need to consider the general form of a parabola oriented in the horizontal direction.
A parabola that opens left or right has the general equation:
[tex]\[ x = a(y - v)^2 + h \][/tex]
Where:
- [tex]\((h, v)\)[/tex] is the vertex of the parabola.
- [tex]\(a\)[/tex] is a constant that affects the width and direction of the parabola.
We will now compare this general form to the given options:
- A. [tex]\( y = a(x - v)^2 + h \)[/tex]
- This equation describes a parabola that opens upward or downward, not left or right.
- B. [tex]\( x = a(y - h)^2 + v \)[/tex]
- This equation has the variables [tex]\(h\)[/tex] and [tex]\(v\)[/tex] swapped incorrectly.
- C. [tex]\( x = a(y - v)^2 + h \)[/tex]
- This equation matches the required form perfectly. [tex]\((h, v)\)[/tex] is the vertex, and it describes a parabola that opens left or right.
- D. [tex]\( y = a(x - h)^2 + v \)[/tex]
- This equation also describes a parabola that opens upward or downward, not left or right.
Thus, the correct equation that describes a parabola opening left or right with the vertex at [tex]\((h, v)\)[/tex] is given by option:
C. [tex]\( x = a(y - v)^2 + h \)[/tex]
