Vertex — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
The turning point — the minimum if it opens up, the maximum if it opens down.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Open — Open excludes the endpoint (<, >); closed includes it (≤, ≥).
What uses it later
This idea is needed for:
- Axis of symmetry — The vertical line through the vertex, x = -b2a.
- Vertex form — y = a(x - h)2 + k, with vertex at (h, k).
Practise this idea
8 questions in the course bank use Vertex, in Graphing Quadratics.
Problem 1
Give the vertex of y = (x - 4)2 + 3.
Worked answer
(4, 3)
h = 4, k = 3
(4, 3)
Problem 2
Give the vertex of y = 2(x + 5)2 - 7.
Worked answer
(-5, -7)
x + 5 means h = -5
(-5, -7)
Problem 3
Find the vertex of y = x2 - 8x + 11.
Worked answer
(4, -5)
x = 82 = 4
y = 16 - 32 + 11 = -5
Problem 4
Find the vertex of y = -x2 + 6x - 5.
Worked answer
(3, 4)
x = -62(-1) = 3
y = -9 + 18 - 5 = 4
Problem 5
Does y = 4x2 - 8x + 1 have a maximum or a minimum?
Worked answer
minimum
The vertex is the lowest point
So a minimum
Problem 6
A ball's height is h(t) = -16t2 + 80t + 6 feet. Find the greatest height.
Worked answer
106
t = -802(-16) = 2.5 s
h(2.5) = -100 + 200 + 6 = 106 feet
Problem 7
For h(t) = -16t2 + 80t + 6, at what time is the height greatest?
Worked answer
2.5
t = 8032 = 2.5 seconds
Problem 8
A parabola has vertex (2, -3) and passes through (5, 6). Find another point on it.
Worked answer
(-1, 6)
(5, 6) is 3 right of the axis x = 2
So 3 left is x = -1
(-1, 6)