If a parabola opens to the right and has its vertex at the origin, what is the g
Practice Questions
Q1
If a parabola opens to the right and has its vertex at the origin, what is the general form of its equation?
y^2 = 4px
x^2 = 4py
y = mx + c
x = ay^2
Questions & Step-by-Step Solutions
If a parabola opens to the right and has its vertex at the origin, what is the general form of its equation?
Step 1: Understand that a parabola is a U-shaped curve. When it opens to the right, it means the arms of the parabola extend towards the right side of the graph.
Step 2: Know that the vertex of the parabola is the point where it turns. In this case, the vertex is at the origin, which is the point (0, 0).
Step 3: The general form of a parabola that opens to the right is given by the equation y^2 = 4px, where 'p' is a positive number that determines how wide or narrow the parabola is.
Step 4: Since the vertex is at the origin, we can use the equation y^2 = 4px directly without any shifts or changes.
Parabola Orientation – Understanding the orientation of parabolas based on their equations, specifically how the direction they open (up, down, left, right) affects their standard forms.
Vertex Form of Parabolas – Recognizing that the vertex of a parabola affects its equation, particularly when the vertex is at the origin.
