C8 - Describe and translate between graphical, tabular, written, and symbolic representations of quadratic relationships

Lindsay

What do these terms mean in plain English?

Graphical: showing the quadratic equation in a graph.

 Tabular: showing the quadratic equation in a table.

Written: showing the quadratic equation in words.

Symbolic Representation: showing the quadratic equation as an equation.

Explanation:

Quadratic Relationships in a graph: In a graph, a quadratic relationship forms a parabola. From this, the vertex, y-intercept and x-intercept(s) can be found. An equation can be found from these points.

Quadratic Relationships in a table: In a table, the pattern for a quadratic relationship can be found. A graph and equation can be made from the data. The data can be any series of numbers that form a quadratic sequence.

Quadratic Relationships in written form: In written form, the relationship is written in words instead of numbers.

Quadratic Relationships in an equation: In an equation, the relationship is shown in numbers. From this, a graph can be made.

Sample Question:

My dad is driving me to my grandmother's house. Within the first hour, he is driving at 50 km/hour. After 6 hours, he is driving at 150 km/hour because he is angry that he's been on the road for 6 hours and he really wants to stop driving. Look at the table below and fill in the blanks. Find the quadratic function for this in a graph and equation then explain in written form.

Solution:

Table solution:

Graph solution:

Equation solution:

D2=5  2a=5  a=2.5

D1=3a+b  10=3(2.5)+b  b=-2.5

tn=a+b+c  50=2.5-2.5+c  c=50

tn=2.5x^2-2.5x+50

Written solution:

The equation for this question is 2.5x to the power of 2 subtract 2.5x plus 50. 50 is the y-intercept and the vertex is (0.5, 49.5) and the stretch is 2.5.