Graphing Quadratic
Equations from the Vertex
Form
Focus 10 Learning Goal –
(HS.A-REI.B.4, HS.F-IF.B.4, HS.F-IF.C.7, HS.F-IF.C.8)
=
Students will sketch graphs of quadratics using key features and solve quadratics using the
quadratic formula.
4
3
2
1
In addition to
level 3, students
make
connections to
other content
areas and/or
contextual
situations
outside of math.
Students will
sketch graphs of
quadratics using
key features and
solve quadratics
using the
quadratic
formula.
- Students will be
able to write,
interpret and
graph quadratics
in vertex form.
Students will be
able to use the
quadratic
formula to solve
quadratics and
are able to
identify some key
features of a
graph of a
quadratic.
Students
will have
partial
success at
a 2 or 3,
with help.
0
Even with
help, the
student is
not
successful
at the
learning
goal.
Graph the following three equations:
y = x2, y = (x – 2)2 and y = (x + 2)2
y = x2
y = (x+2)2
y = (x-2)2
 How are the graphs of these equations similar?
 How are they different?
 Vertex (0, 0) and (0, 2) and (0, -2)
 The graphs are translations of each other.
www.demos.com/calculator
Use the graphing calculator on this website and type
in each of the three equations we just graphed by
hand:
y = x2
y = (x – 2)2
y = (x + 2)2
When you need to make the exponent, use ^ button
(shift, 6)
Consider the graph of y = (x – 5)2.
Where would you expect this graph to
be in relation to y = x2 ?
 We would expect this
graph to be 5 units to
the right of y = x2.
 Consider the graph of
y = (x + 5)2. Where
would you expect this
graph to be in relation
to y = x2?
 5 units left of y = x2.
Use the graphing website and graph
the following equations:
y = x2 +3
y= x2 – 3
y = (x + 2)2 - 3
What do you notice about the vertex on each one?
(0, 3) then (0, -3) then (-2, -3)
Based off the equation, determine a way to find the vertex of each
quadratic without using a graphing calculator or graph paper.
Without graphing, state the vertex of
each quadratic:
1. y = (x – 5)2 + 3
1. (5, 3)
2. y = x2 – 2.5
1. (0, -2.5)
3. y = (x + 4)2
1. (-4, 0)
4. y = (x + 9)2 – 6
1. (-9, -6)
The simplified vertex form of the quadratic equation is:
y = (x – h)2 + k, where (h, k) is the vertex.
Write a quadratic, in vertex form, whose
graph will have the given vertex:
1. (1.9, -4)
1. y = (x – 1.9)2 – 4
2. (0, 100)
1. y = x2 + 100
3. (-2, 3/2)
1. y = (x + 2)2 + 3/2
Try the following equations on the graphing
calculator. Determine the effect of a leading
coefficient.
1. y = (x + 2)2 + 1.5
2. y = -½(x + 2)2 + 1.5
3. y = ½(x + 2)2 + 1.5
4. y = 2(x + 2)2 + 1.5
5. y = -2(x + 2)2 + 1.5
1.
4.
2.
5.
3.
 The vertex is (-2, 1.5) for all five
graphs.
 When “a” the number in front of the
parenthesis is between -1 and 1, the
graph is wide.
 When “a” is less than -1 or greater
than 1, the graph is narrower.
 What about when “a” is positive or
negative?
When graphing a quadratic
equation in vertex form,
y = a(x – h)2 + k, (h, k)
are the coordinates of
the vertex.