For a Maths Studies exam question you need to know how to draw a quadratic graph and to know the names of key parts of the graph.
For SL you need to know the same things as pre-learning
A Quadratic Graph
Quadratic means related to squares, and a quadratic graph has an x2 (x-squared) term in it. This is a hint to remember what quadratic means.
The ∪ or ∩ shape is called a Parabola
The Vertex is the minimum point or minimum (sometimes the maximum point)
The y-intercept point is the point where the curve cuts the y-axis
The x-intercept points are the points where the curve cuts the x-axis
There may be 2, 1 or 0 x-intercept points. 2 if the minimum point is below the x-axis, 1 if it is on the s-axis, and 0 if it is above.
Intercept wording – be careful
Intercept = Intercept Point BUT Intercept ≠ Intercept Value
for the graph above: y-intercept point = (0,5)
y-intercept value = 5
y-intercept = (0,5)
IB exams are unusual because you must remember that intercept alone means the co-ordinates, e.g. (0,5). This is true for Maths Studies, Maths SL/HL, and even for some other subjects like Economics HL.
The Intercept value is useful when we go back to the equation.
For y= x2 – 6x + 5 the y-intercept value is +5
and generally for y= a x2 – bx + c the y-intercept value is c
This is because on the y-axis x=0, and when x= 0 then y = 0 + 0 + c = c
For y= x2 – 6x + 5 the x-intercept value are 1 and 5
When x=1 or x=5 then y =0
The x-intercept values (sometimes called the zeroes) are the solutions of
the equation 0= x2 – 6x + 5
∩-shaped parabolas are drawn when the x2 term is minus
∪ shaped or ∩ shaped Parabola?