Document page
mathematicsprinted 42 · PDF 43
165 pagesrevision 46935
printed 42 · PDF 43
Page image rendered from the stored file at 110 dpi; it sharpens as you zoom. Outlines are placed from each region’s stored position on the page (595 × 842 pt).
readable
Source of this text: embedded text layer. The better of the embedded text and OCR is kept.
42
Interpreting Graphs
Interpreting graphs involves understanding what the shape of a curve represents in
real life situations. We should also understand what slope means and how to
interpret what a high or low slope value represents. An understanding of plotting
points is also important. Graphs communicate important quantitative information in a
visual format. Using this form of representation, students must be able to:
● Elicit key information
● Extract the basic information
● Draw conclusions
● Compare and contrast situations and
● Provide recommendations.
Solution of Equations
Accurately drawn graphs enables us to find approximate solutions to a wide range of
equations, many of which are impossible to solve exactly ‘conventional’ methods.
● Draw the graph of a given function for given range.
● To find the solutions of equation rearrange the equation so that the function
already plotted is on one side.
● Draw the graph for the other side of the equation.
● Now the values of the point of intersection are the solutions of the equation.
Distance-Time Graph
When a distance-time graph is drawn the gradient of a graph gives
the speed of an object. (Because)
● O to A: constant speed
● A to B: speed goes down to zero
● B to C: at rest
● C to D: accelerates (speed is increasing)
● D to E: constant speed (not as fast as O to A)
Speed-Time Graph
When a speed-time graph is drawn the gradient of a graph gives the acceleration of
an object and area under the graph tells us about the distance travelled by that
object. (
Turning Points
A turning point (also known as stationary point) is a point on a graph where the
gradient is zero. One method that can be used to find the turning points of a certain
graph is completing the square method. When the quadratic function is written in the
form the coordinates of the turning point on the graph are (a, b). This method is
used to find the turning points on a quadratic graph, but for other graphs (for
example cubic graphs) this does not work. For such graphs we use gradient
functions.
Gradient Functions