MPM 2D
Date:
Quadratics Part 3 – Vertex Form
Forms of Equations:
1. Standard Form y  ax 2  bx  c
(Expanded Form)
2. Factored Form y  a( x  s )( x  t )
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Can determine the direction of opening
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Direction tells us whether we have a min or max
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Determine the zeros
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Determine the location of the vertex
3. Vertex Form y  a( x  h)2  k
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Determine the vertex by simple inspection
Determine the ‘a’ knowing vertex and one other point
Determine the direction of the opening by the value of ‘a’
Can convert to standard form by expanding and collecting like
terms
Remember: When a>0
When a<0
Equation
Direction
of
Opening
Relative Width
(compare x2)
Coordinates
of
Vertex
y  x2
y  ( x  3)2  2
y  3( x  4)2  3
y  2( x  1)2  5
Working with Vertex Form
1. Given equation
1
y   ( x  5) 2  3
2
a) State ‘a’ and the direction of opening
b) What is the vertex
Equation of
Axis of
Symmetry
a
h
k
MPM 2D
Date:
2. Find, in vertex form, the equation of the quadratic relation with vertex at
(5,-3) and passes through the point (1,-8).
3. Given equation y  2( x  3)2  7
a) If vertex is (-3,-7) find two other points on the parabola
Hint: Choose a value for ‘x’ that is reasonably close to axis of symmetry, then
substitute into the equation and solve for y.