MPM2D
Vertex Form
GRAPH VERTEX FORM
(
Quadratic Relations
)
LEARNING GOALS


Review how to transform
for a given quadratic relation.
Review how to graph using the vertex form of a quadratic relation.
TRANSFORMATIONS
Consider the quadratic equation in vertex form
Starting with the graph of
equation.
(
)
.
, we can develop the steps required to transform to the above
A. Step 1: Graph
(Include at
least the points -2,-1,0,1,2).
B. Step 2: Inversion
a. Is a < 0?
If so, complete the
inversion of the original
graph and label the new
line.
C. Step 3: Stretch
a. Is -1 < a < 1?
b. Is the value of a > 0
(not including a negative
sign)?
If so, multiply each yvalue by a factor “a”.
D. Step 4a: Horizontal Shift
a. Is h > 0 or h < 0?
If so, shift the graph horizontal by a value of h.
*Step 4a and 4b can be done
simultaneously.
E. Step 4b: Vertical Shift
a. Is k > 0 or k < 0?
If so, shift the graph
vertically a value of k.
PRACTICE
Complete the transformation steps on
the graph to the right for
(
)
.
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MPM2D
Vertex Form
Quadratic Relations
VERTEX FORM FROM A GRAPH
Find the equation that represents the graph to
the right.
A. Step 1: Vertex
a. Looking at the graph, what is the
vertex?
b. Is the y-value of the vertex a
maximum or a minimum?
c. What is the axis of symmetry?
d. Using the vertex, what is the
equation of that represents the
curve?
* Notice you are not able to complete the equation without a value for “a”.
B. Step 2: Find a point on the curve
a. In order to find the value of “a”, you need a second point along the curve. The
most obvious points to check are the x- and y-intercepts.
What is the most appropriate point along this curve you can use?
C. Step 3: Solve for the stretch factor “a”.
a. Using the point you found in Step 2, solve for the stretch factor.
D. Step 4: Final Equation
a. What is the equation in vertex form that represents the curve from the graph?
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MPM2D
Vertex Form
Quadratic Relations
PRACTICE
An Olympic swimmer is practicing for an upcoming event. Their coach records their initial dive to
help determine how they can achieve a better start to the beginning of the race. The swimmer
starts from a diving board that is 0.5 m from the surface of the water and dives down to a depth
of 1.5 m below the surface of the water at a point 2 m from the edge of the board.
A. Find the quadratic relation in
vertex form that represents
the dive.
B. How far from the diving board does the swimmer surface after the dive?
C. Is there another point where the swimmer is at the surface of the water? If so, where?
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MPM2D
Vertex Form
Quadratic Relations
SUMMARY
You can find the following pieces of information from the quadratic relation;
(
Vertex of the parabola is (
)

The

h represents the _______________ translation of h units.
k represents the ________________translation of k units.
The axis of symmetry of the parabola is the _________________ line through
the ___________ with the equation
.
a represents the vertical stretch or compression factor relative to the graph of
o If a>0, the parabola opens ____________ and the vertex is also the



,
).
______________ point.
o
If
a<0 the parabola opens ____________ and the vertex is also the
______________ point.
o
When
-1<a<1 then the parabola is compressed vertically.
HOMEFUN 
P185 Q1(d-h), 2-11
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