Answer:
f(x) = ¼ x² + ⁵/₂ x + ²⁵/₄
Step-by-step explanation:
b² = 4ac, so the discriminant is 0. That means the quadratic has a repeated root, which is the vertex.
f(x) has an axis of symmetry of x = -5. That means the x-coordinate of the vertex is -5.
So f(x) = a (x + 5)².
f(-1) = 4, so the value of a is:
4 = a (-1 + 5)²
4 = 16a
a = ¼
The function is f(x) = ¼ (x + 5)². Converting to standard form:
f(x) = ¼ (x² + 10x + 25)
f(x) = ¼ x² + ⁵/₂ x + ²⁵/₄
