Answer:
f(x) = 2x^2 - 16x + 35
Explanation:
To find the equation of the quadratic function, we need the vertex V and a point P that lies on the function.
Given:
Vertex V: (4, 3)
Point P: (-4, 131)
The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
Where (h, k) represents the vertex.
Using the vertex V (4, 3), we have:
h = 4
k = 3
Substituting these values, we get:
f(x) = a(x - 4)^2 + 3
Now, we can use the point P(-4, 131) to find the value of 'a'.
Substituting x = -4 and y = 131 into the equation:
131 = a(-4 - 4)^2 + 3
131 = a(-8)^2 + 3
131 = a * 64 + 3
131 - 3 = 64a
128 = 64a
a = 128 / 64
a = 2
Now, substituting the value of 'a' back into the equation:
f(x) = 2(x - 4)^2 + 3
Expanding and simplifying:
f(x) = 2(x^2 - 8x + 16) + 3
f(x) = 2x^2 - 16x + 32 + 3
f(x) = 2x^2 - 16x + 35
Therefore, the equation of the quadratic function in standard form, with vertex (4, 3) and passing through point (-4, 131), is:
f(x) = 2x^2 - 16x + 35