4.2 Completing the Square

Ex 1 Discuss the transformations on the following graphs

(a) y = 4(x - 3)^2 - 5 (b) y = -(x + 2)^2 - 3

(c) y = -3x^2 + 5x

Completing the Square is a process where you can change a quadratic from standard form (y = ax^2 + bx + c) to vertex form (y = a(x - h)^2 + k)

Steps

1. Factor out the leading coefficient from the first two terms
2. Divide the coefficient of the x term by 2 and then square it; add and subtract this number after the x term.
3. Remove the negative number from (2) from the brackets by multiplying it by the number from (1)
4. Factor and simplify.

Ex 2 Complete the Square

(a) y = x^2 + 12x - 7 (b) y = x^2 + 3x + 1

(c) y = 2x^2 + 12x (d) y = 10 - 10x - x^2

(e) y = 2x^2 + 3x + 2 (f) y = -3x^2 + 4x

(g) y = -(1/3)x^2 + 2x + 4 (h) y = 0.2x^2 + 1.6x + 3.1

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