**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.

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