M and C are constants.
The gradient = M The intercept on the y axis = C
Gradient = Ystep/ X step
Graph mode, Enter equation, Draw, G-Solve = Y intercept
Models of direct proportion
Variables X and Y are in direct proportion if Y=kX
The graph of Y against X is a STRAIGHT LINE, with gradient k, which passes through the origin (0,0).
k often gives a significant measure, e.g for a currency conversion graph k gives the rate of exchange.
a,b and c are constants.
You can make every possible quadratic function by changing the values of a,b and c.
Completeing the square gives the form Y=m(x+n)²+ p
If m is positive, the function has a minimum value of p, when x=-n.
If m is negative, this function has a maximum value of p, when x= -n.
Quadratic equations can be solves by:
- Using a graph
- Completing the square
- Using the formula x= -b±√ b² - 4ac / 2a
Quadratic models can be used to model all or part of a set of data.
Quadratic graphs have either a single minimum point or a single maximum point.
Y= ax²+ bx +c
Graphs can be used to solve equations by finding the x co-ordinates of the points of intersection with the x axis or other lines.
Graph mode, Enter equation, Draw, G-Solve, roots = points of intersection.
Roots- The solution when y=0, or the x-axis interception (cross)
Minimum- Lowest value
Maximum- Highest value
Turning points- Minimum/maximum
Line of symmetry- Line of which both sides are symmetrical
Y intercept- Point of which the graph crosses the y axes.
Real life situation/s:
degrees/B = Period
C= phase shift
D= vertical shift