Answer:
see explanation
Step-by-step explanation:
To find a , substitute the coordinates of the point on the curve into the equation, that is
(1)
y = ax² (3, 18)
18 = a × 3² = 9a ( divide both sides by 9 )
2 = a , then
y = 2x² is the equation
(2)
y = ax² (- 2, 30 )
30 = a × (- 2)² = 4a ( divide both sides by 4 )
7.5 = a , then
y = 7.5x² is the equation
(3)
y = ax² (4, 8 )
8 = a × 4² = 16a ( divide both sides by 16 )
[tex]\frac{8}{16}[/tex] = [tex]\frac{1}{2}[/tex] = a , then
y = [tex]\frac{1}{2}[/tex] x² is the equation
(4)
y = ax² (- 1, - 2 )
- 2 = a × (- 1)² = a , then
y = - 2x² is the equation
(5)
y = ax² (2, - 12 )
- 12 = a × 2² = 4a ( divide both sides by 4 )
- 3 = a , then
y = - 3x² is the equation
(6)
y = ax² (- 3, - 3 )
- 3 = a × (- 3)² = 9a ( divide both sides by 9 )
[tex]\frac{-3}{9}[/tex] = - [tex]\frac{1}{3}[/tex] = a , then
y = - [tex]\frac{1}{3}[/tex] x² is the equation
