What is the vertex form of a function with the vertex -3,-4 and point -2,-3
To determine the vertex form of a quadratic function with the given vertex (-3,-4), we can use the general equation for a vertex form parabolic function:
y = a(x-h)^2 + k
Where (h,k) is the vertex of the parabola.
Using the given vertex (-3,-4), we can substitute h = -3 and k = -4 into the equation:
y = a(x+3)^2 - 4
To find the value of 'a', we can use the additional point (-2, -3) on the parabola. Substituting x = -2 and y = -3 into the equation:
-3 = a(-2+3)^2 - 4
-3 = a(1)^2 - 4
-3 = a - 4
a = -3 + 4
a = 1
Therefore, the vertex form of the function is:
y = (x+3)^2 - 4