Final answer:
After substituting the vertex (-1,5) into the vertex form of a quadratic equation and using the point (3,-19) to solve for 'a', the quadratic function is found to be y = -1.5(x + 1)² + 5.
Step-by-step explanation:
To find a quadratic function with a given vertex of (-1, 5) and containing the point (3, -19), we can use the vertex form of a quadratic function, which is:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola. Here, h = -1 and k = 5. Next, we substitute the vertex into the equation, resulting in:
y = a(x + 1)² + 5
We also know the function contains the point (3, -19). Substituting x = 3 and y = -19 into the equation gives us:
-19 = a(3 + 1)² + 5
Solving for a, we get:
-19 = a(4)² + 5
-19 = 16a + 5
-24 = 16a
a = -24/16 = -1.5
The quadratic function is therefore:
y = -1.5(x + 1)²+ 5
The complete question is: Find a quadratic function that has a vertex of (-1, 5) and contains the point (3, -19) is: