Answer to Question #269031 in Algebra for Paul Carpenter

Question

Reflect on the concept of lines and quadratic functions. What concepts (only the names) did you need to accommodate the concept of lines and quadratic functions in your mind? What are the simplest line and quadratic function you can imagine? In your day to day, is there any occurring fact that can be interpreted as lines and quadratic functions? What strategy are you using to get the graph of lines and quadratic functions?

Answer 1

a) Concept : Degrees of polynomial

For a line the degree of polynomial = 1

For the quadratic function; degree of polynomial > 1

b) Simplest line form

y = mx + c

Quadratic function

y = ax²+ bx + c

c)

i)Day to day example of a line is of a bus fare which comprises of both fixed costs and variable costs for every kilometre covered.

Therefore;

Line function for the total fare will be

y = mx + c where c is the fixed cost

m is the variable cost for every kilometre covered

x is the total distance covered in kilometre

ii) Likewise day to day example of a quadratic function is the the sports events such as javelin, football, and shotput where the ball follows a parabola trajectory governed by a quadratic function.

d)

i) For a graph of line, two points are only needed to assist in drawing a line.

ii) For a quadratic function, vertex such as x-intercept and y-intercept are needed.