Final answer:
To obtain the equation of a parabola with a given vertex and point, substitute the vertex into the vertex form of a parabola's equation and use the point to solve for the coefficient a. For the vertex (-2, 5) and point (2, 9), the resulting equation is y = (1/4)(x + 2)^2 + 5.
Step-by-step explanation:
To find the equation of a parabola with vertex (-2, 5) that contains the point (2,9), we can use the vertex form of a parabola's equation: y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Given the vertex (-2, 5), we substitute h and k into the equation, resulting in y = a(x + 2)^2 + 5. Then we use the point (2, 9) to find the value of a. Substituting x = 2 and y = 9 gives us 9 = a(2 + 2)^2 + 5. From this, we can solve for a:
9 = a(4)^2 + 5
9 = 16a + 5
4 = 16a
a = 4 / 16
a = 1/4
Thus, the equation of the parabola is y = (1/4)(x + 2)^2 + 5.