# S-Cool Revision Summary

## S-Cool Revision Summary

## Linear graphs

Linear functions can be written in the form **y = mx + c** where y and x are variables and m and c are constants (numbers).

If you write them like this then **m** is the **gradient** and **c** is the **y-intercept** (point where it crosses the y-axis). The graphs of linear functions are **straight lines**.

**To find m:**

Pick any two points.

**To find c:**

c is the point where the graph crosses the y-axis.

## Quadratic graphs

Quadratic functions can be written in the form:

**y = ax ^{2} + bx + c**

where a, b and c are constants and 'a' doesn't equal zero.

Quadratic graphs are always **parabolas** ('U' shapes).

The really important bits of a quadratic are:

**Where it turns (the bottom of the 'U')**

**Where it crosses the x-axis (if it does!)**

The solutions of a quadratic are where the graph crosses the x-axis!

## Cubic and reciprocal graphs

**You need to be able to:**

- Plot and draw these.
- Recognise the shapes.
- Read the solutions from the graph (cubics only).

*Cubics* can be written in the form:

**y = ax ^{3} + bx^{2} + cx + d**

*Reciprocals* are where the x is on the bottom of a fraction.

Drawing their graphs - **Table - Axes - Plot - Draw - Label**

The *solutions* of a cubic are where it crosses the x-axis and it can have up to 3.

## Graphs of simultaneous equations

As simultaneous equations at GCSE are **linear** (can both eb written in the form y = mx + c) their graphs will be straight lines.

The solution (x-value and y-value) is where the straight lines intersect (cross one another).

## Inequalities - regions on a graph

**To draw a graph:**

- Change the inequality sign to an '=' sign.
- By choosing 4 or 5 different values for x, make a table of co-ordinates.
- Draw and label the line (make it dotted if the inequality sign is < or >).
- Choose a test point (not on the line!).
- Put the x and y values of the test point into the inequality.
- If it works, shade and label that side of the line with the inequality.
- If it doesn't work, shade and label the other side.

## Travel graphs

*Distance/time*

If you show a graph of a journey showing distance travelled (on the y-axis) against time (on the x-axis):

- The
**gradient**(or slope) of the graph represents the**speed**. - A horizontal section indicates that you have stopped.
- A section sloping up means that you are going away.
- A section sloping down means you are coming back.
- The steeper the line, the faster you are going.

*Speed/time*

- The
**gradient**(or slope) of the graph represents the**acceleration**. - The
**area**under the graph (for any section) is the**distance travelled**(in that section). - A horizontal section indicates constant speed (no acceleration).
- A section sloping up means accelerating.
- A section sloping down means slowing down.
- The steeper the line, the quicker the acceleration.