Final answer:
The equation for a parabola centered at (0,0) that goes through the point (3, 45) is y = 5x². The coefficient 'a' is found by substituting the point into the standard form y = ax² and solving for 'a'.
Step-by-step explanation:
To write the equation for a parabola centered at (0,0) that goes through the point (3, 45), we use the standard form of a parabola's equation, which is y = ax² for a parabola that opens upwards or downwards. Given that the parabola is centered at (0,0), there is no need to include horizontal or vertical shifts in the equation.
Using the point (3, 45), we can substitute these values into the equation to find the coefficient 'a':
- y = ax²
- 45 = a(3)²
- 45 = 9a
- a = 45 / 9
- a = 5
Therefore, the equation of the parabola is y = 5x².