find th quadratic fuction that has a vertix of (8.-3) and whose graph goest throught the point (-6, -395)
you know the function has to be
y = a(x-8)^2 - 3
sub in (-6,-395) to find the value of a
To find the quadratic function with a vertex and a point that it passes through, we can use the vertex form of a quadratic function.
The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
1. Start by substituting the vertex coordinates into the vertex form equation: f(x) = a(x - 8)^2 - 3
2. Next, we'll use the given point (-6, -395) to solve for 'a'. Plug in the x and y values of the point into the equation we obtained in step 1.
-395 = a(-6 - 8)^2 - 3
3. Simplify the equation.
-395 = a(-14)^2 - 3
-395 = a(196) - 3
-395 = 196a - 3
4. Solve for 'a'.
196a = -395 + 3
196a = -392
a = -392/196
a = -2
5. Substitute the value of 'a' back into the vertex form equation to find the quadratic function.
f(x) = -2(x - 8)^2 - 3
So, the quadratic function that has a vertex of (8, -3) and passes through the point (-6, -395) is f(x) = -2(x - 8)^2 - 3.