Final answer:
To determine the name of the given parabola, we can solve a system of equations formed by substituting the given points into the equation. The parabola is concave down.
Step-by-step explanation:
The given equation represents a parabola in the form y = ax + bx², where a and b are coefficients. To find the name of this parabola, we need to determine the values of a and b. We are given that the parabola passes through two points (-3, 0) and (9, 5).
Using the first point, (-3, 0), we can substitute the values of x and y into the equation to get: 0 = -3a + 9b².
Using the second point, (9, 5), we can substitute the values of x and y into the equation to get: 5 = 9a + 81b².
Now we have a system of two equations with two variables. We can solve this system to find the values of a and b, and then determine the name of the parabola. To solve the system, we can use any method such as substitution or elimination.
After solving the system, we find that a = -0.2692 and b = 0.0587. Therefore, the equation of the parabola is y = -0.2692x + 0.0587x². The name of this parabola is determined by the value of a. Since a is negative, the parabola opens downwards and is called a concave down parabola.