Formative assessment

Question

The quadratic function shown has a form f(x) = (x+h)^ + k.

Determine the values of h and k.

Point A is the positive zero of f(x).  Algebraically, determine its  value to the nearest hundredth.  Show how you arrived at your answer.

 

Thank you for your help.

Answer 1

Let's rewrite f(x) = (x + h)^2 + k as (x - (-h))^2 + k. Why? It allows us express h in terms of a and b.

 

h is traditionally -b/2a where a = coefficient of x² and b = coefficient of x. So, -h = b/2a.

 

The vertex form of a parabola is a(x - h)^2 + k and (h, k) is the vertex.

 

h represents horizontal shift and k represents vertical shift or y-intercept (when x = 0).  If x = 0, f(x) = h² + k, and the function is now an expression of h such that f(h) = k.