MPM 2D
VERTEX FORM of a QUADRATIC FUNCTION
Up to this point in the QUADRATIC FUNCTIONS unit, you have usually worked with the standard form
of the quadratic function. You have seen it written as
or in factored form as
The standard form of the quadratic function is very useful in predicting the _________ _________ of
projectiles and _______________ other real-life situations. This is because the constant __ in the
function is always the _______________ of the graph.
The _____________ of the quadratic function is very useful in predicting the ___________ a projectile
will hit the ground in real-life situations. This is because the factored form reveals the
______________.
Another form that a quadratic may be written in is __________________:
_____________________________
In both the _____________form and the ______________form, there is a variable raised to the
_________________ power and the highest power of a variable is ___, so it is easy to recognize them
as quadratic functions.
The vertex form is excellent for modelling situations where the ______________ or _____________
value is important. The vertex form enables you to _____ the maximum height of a jump _________
_________________ than the standard form of a quadratic function does.
The vertex occurs at the ______________ (axis of symmetry) at the ___________ or _________ point
on the curve.
The _____________ is revealed ______________ in this form.
To continue you will need to be able to identify each letter in the formula:
Given:
y= -3(x-8)2 +3 compare it to
y = a(x - h)2 + k
Fill in what
a= ______ h=_______ k=______
Now try these on your own.
For y= (x-5)2 - 2
What are a= ______ h=_______ k=______
And y= 4(x+5)2 + 1
What are a= ______ h=_______ k=______
Go to the next page and use this website to complete the worksheet:
http://www.mathopenref.com/quadvertexexplorer.html
Vertex form
Vertex form of the quadratic relation can be used to describe any transformation of y  x 2
2
y

a
(
x

h
)
k
Vertex form of a quadratic relation is:
Enter each of the following parabolas into the computer app and identify the vertex.
Relation
Vertex
y  x2
Using the letters of the general formula above, what is the vertex in
every case?
y  ( x  5)2  4
y  ( x  5)2  4
Vertex = (
,
)
y  ( x  8)  3
2
y  ( x  2)2  1
y  ( x  2)2  8
y  ( x  7)2  2
To fill in the chart BELOW, use the computer app to help you to fill in the first empty row of the
table. YOU SHOULD SEE A PATTERN. YOU WILL NO LONGER NEED THE APP TO DO THE REST, ONCE
YOU SEE THE PATTERN. Do the rest without the computer!
Relation
Direction of
Opening (up
or down)
Vertex
Axis of
Symmetry
Optimal
Value
Maximum or
Minimum
y  2( x  2)2  1
y  2( x  3)2  1
1
( x  6) 2  3
2
1
y   ( x  6) 2  5
2
y
y  a ( x  h) 2  k
2
y

a
(
x

h
)
k
Explain what each letter in the formula reveals:
Use the computer app to help you explain what the value of “a” does to the curve. Always compare
each new curve to the standard shape of y=x2
Relation
y = x2
What does the “a” do
In relation to the shape of the curve
Plot this curve using the computer app.
This is the standard shape of the parabola.
Compare all the following curves to this shape.
y  2( x  2)2  1
y  2( x  3)2  1
1
( x  6) 2  3
2
1
y   ( x  6) 2  5
2
y
𝑦 = (𝑥 − 5)2 − 4
Make a general rule about value of “a” in the quadratic, include the value and the sign in
your answer: