Question

Each equation given below describes a parabola. Which statement best compares their graphs?
x= 5y^2 x=3y^2

a. both parabolas open upward and x=5y^2 is wider than x= 3y^2

b. both parabolas open to the righ and x=3y^2 is wider than x=5y^2 .

c. both parabolas open upward and x=3y^2 is wider than x=5y^2

d. both parabolas open to the right and x=5y^2 is wider than x=3y^2

Answer 1

which way do they open?

Answer 2

right @pgpilot326

Answer 3

okay, so which one gets to x = 20 first?

Answer 4

x=5y^2

Answer 5

right, it gets there when y = 2 or -2. the other equation needs more y, meaning it's going to be... wider or skinnier?

Answer 6

wider @pgpilot326

Answer 7

Comparing the graphs by drawing \(x=15\), we get,

For \(x=3y^2\), \(y=\sqrt5,-\sqrt5\)
For \(x=5y^2\), \(y=\sqrt3,-\sqrt3\)

Thus,

\(1)\) Any \(x=ay^2\) is open to the right, if \(a>0\), and open to the left, if \(a<0\).

\(2)\) For \(x=ay^2\) and \(x=by^2\), or \(y=ax^2\) and \(y=bx^2\), latter parabola is wider if \(|a|>|b| \) , and latter is slicker if \(|a|<|b| \).

\(3)\) \(y=ax^2\) is open upward if \(a>0\) and downward if \(a<0\).