Question

Which of the equations below could be the equation of this parabola?++-6VertexO A. y ----²○ B. x=-=y²O c. x==y²O D. y = ¹x²6(0, 0)10S

Answer 1

A horizontal parabola is given with vertex at (0,0).

It is required to determine which of the equations could be the equation of the parabola.

The standard form of the equation of a parabola with vertex at the origin (0,0) is given as:

`x=ay^2`

Where a is a constant to be determined.

Notice from the graph that it passes through the point (1,2).

Substitute (x,y)=(1,2) into the equation:

`\begin{gathered} 1=a(2)^2 \\ \Rightarrow1=4a \\ \Rightarrow a=(1)/(4) \end{gathered}`

Substitute a=1/4 back into the equation:

`x=(1)/(4)y^2`

Hence, the answer is