Question

find the correct equation. make sure the purple ball goes through the stars.

Answer 1

SOLUTION

Equation of a parabola is given by the form

$\begin{gathered} y=a(x-h)^2+k \\ \text{where h and k are coordinates of the vertex } \end{gathered}$

From the first one given to us which is

$\begin{gathered} y=0.03\mleft(x-15\mright)^2+20\mleft\{x<15\mright\} \\ \text{The vertex is }(15,20) \\ \text{while }\{x<15\}\text{ means values of x less than 15} \end{gathered}$

The other stars (vertices) have coordinates of

$\begin{gathered} (15,15) \\ (15,10) \\ (15,5) \end{gathered}$

So replacing these coordinates to be like the first equation, we have

$\begin{gathered} y=0.03\mleft(x-15\mright)^2+15\mleft\{x<15\mright\} \\ y=0.03\mleft(x-15\mright)^2+10\mleft\{x<15\mright\} \\ y=0.03\mleft(x-15\mright)^2+5\mleft\{x<15\mright\} \end{gathered}$

Hence the answer is

$\begin{gathered} y=0.03\mleft(x-15\mright)^2+15\mleft\{x<15\mright\} \\ y=0.03\mleft(x-15\mright)^2+10\mleft\{x<15\mright\} \\ y=0.03\mleft(x-15\mright)^2+5\mleft\{x<15\mright\} \end{gathered}$