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5.3 Converting from Standard to Vertex Form (4.4 in text)
Completing the Square
A method to convert a quadratic
equation from standard form to
vertex form (without using the zeros!!)
Convert y = -2x 2 +12x – 7 to vertex form by completing the square:
Step 1: Factor the coefficient of the
x 2 -term from the first TWO
terms. (only the first 2 terms)
y = -2x 2 +12x – 7
Step 2: Find the constant that must be
added or subtracted to create
a perfect square trinomial.
TIP: it is the square of half the
coefficient of the x-term after
the coefficient is factored out.
** So take the number in front of x, divide by 2 and square it
Step 3: ADD this term inside the brackets.
BUT you must keep the equation
balanced by then SUBTRACTING
that same number inside the brackets.
**So just add and subtract the same number
Step 4: Group the 3 terms that form the
perfect square. Move the subtracted
value OUTSIDE the brackets (but you
must MULTIPLY it by the coefficient
FIRST!!)
** multipy the 4th term and remove it from the bracket
Step 5: Factor the perfect square trinomial.
Collect like terms. The end!
Find the vertex for each quadratic relation.
a) y = 2 x 2 + 20x + 43
HW. p. 234 #2ace, 5ac, 7ace, 9ace, 14 - 16
b) y = 3 x 2 - 6x + 13
c) y = 0.2 x 2 - 10x + 650