Open — Grade 7 Accelerated, what it means and where it is taught
Open excludes the endpoint (<, >); closed includes it (≤, ≥).
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Closed dot — Open excludes the endpoint (<, >); closed includes it (≤, ≥).
- Vertex — The turning point — the minimum if it opens up, the maximum if it opens down.
Practise this idea
12 questions in the course bank use Open, in Solving Inequalities, Linear Inequalities, Graphing Quadratics, Absolute Value, Piecewise & Step Functions, Parent Functions & Transformations, Conic Sections. The first 8 are below; the rest are in those units.
Problem 1
On a number line, which dot do you use for x > 5?
- A closed (filled) dot
- An open (hollow) dot
Worked answer
An open (hollow) dot
x > 5 does not include 5 itself, so the dot is open.
Problem 2
Which dot do you use for x ≥ 3?
- A closed (filled) dot
- An open (hollow) dot
Worked answer
A closed (filled) dot
3 itself is a solution, so the dot is closed.
Problem 3
For the solution x ≥ 4, is the circle at 4 open or filled?
Worked answer
filled
x = 4 is a solution
So the circle is filled
Problem 4
Does y = 3x2 - 5x + 1 open up or down?
Worked answer
up
a = 3 > 0
So it opens upward
Problem 5
Does y = -2x2 + 7 open up or down?
Worked answer
down
a = -2 < 0
So it opens downward
Problem 6
Does y = 4x2 - 8x + 1 have a maximum or a minimum?
Worked answer
minimum
The vertex is the lowest point
So a minimum
Problem 7
The graph of y = -|x| + 2 has a vertex at (0, 2) and
- opens downward
- opens upward
- is a straight line
- is a parabola
Worked answer
opens downward
-|x| turns the V upside down
So (0, 2) is a maximum
Problem 8
A parabola has vertex (-1,4) and opens upward, same width as y=x2. Write its equation.
Worked answer
y=(x+1)^2+4
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