Question

Axis of parabola is \( x = 0 \). If the vertex is at a distance of 3 from the origin above the x-axis, find the vertex.

• A. \( (0, 3) \)
• B. \( (3, 0) \)
• C. \( (0, -3) \)
• D. \( (-3, 0) \)

Hint:

The axis of symmetry helps in determining the value of \( h \), and the distance from the axis to the vertex gives the value of \( k \).

Answer 1

The Correct Option is A

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex. The axis of symmetry is the line \( x = h \). Given that the axis is \( x = 0 \), this implies \( h = 0 \). The vertex is a distance of 3 units above the x-axis, so \( k = 3 \). Therefore, the vertex is \( (0, 3) \).