Question

12. Determine the rule of the quadratic functionſ

given the following information:
• When f(x) = ax^2+ bx+c, b2 = 4ac
• f(x) bigger than or equal to 0 for XER
• f(x) has an axis of symmetry of x = -5
• f(-1)=4

Answer 1

f(x) = ¼ x² + ⁵/₂ x + ²⁵/₄

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