Final answer:
The formula for the quadratic function with a vertex at (7,8) and a y-intercept at y = -6 is y = -(2/7)(x - 7)^2 + 8.
Step-by-step explanation:
To find the formula for the quadratic function with a vertex at (7,8) and a y-intercept at y = -6, we use the vertex form of a quadratic equation, which is y = a(x - h)² + k, where (h,k) is the vertex.
Since we know the vertex, we can start with y = a(x - 7)² + 8. To find the value of 'a', we will use the y-intercept.
Substitute y with -6 (the y-intercept) and x with 0 (because the y-intercept occurs when x is 0) in the equation:
-6 = a(0 - 7)² + 8
-6 = 49a + 8
To solve for 'a', subtract 8 from both sides and then divide by 49:
-14 = 49a
a = -14 / 49
a = -2/7
Now we substitute 'a' back into the vertex form:
y = -(2/7)(x - 7)² + 8
This is the quadratic function for the given vertex and y-intercept.