x2+6x+9 = x+3
x2+6x-x+9-3 = 0
x2+5x+6 = 0
Solve by factoring or with the help of the quadratic equation formula:
(x+3)(x+2) = 0
Therefore: x = -3 or x = -2
(3, -21)
x2 + 6x = 7 ⇒ x2 + 6x + 9 = 7 + 9 ⇒ (x + 3)2 = 16 ⇒ x + 3 = ±4 ⇒ x = -7 or 1
x2 + 6x + 1 = 0 x2 + 6x + 9 = 8 (x + 3)2 = 8 x + 3 = ± 2√2 x + 3 = -3 ± 2√2 x ∈ {-3 - 2√2, -3 + 2√2}
y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7
x2-6x+9 = (x-3)(x-3) when factorised.
x2 + 6x + 12 = 0 x2 + 6x + 9 = -3 (x + 3)2 = -3 x + 3 = ± √-3 x = -3 ± i√3
x2 + 6x - 2 = 0 x2 + 6x + 9 = 13 (x + 3)2 = 13 x + 3 = ± √13 x = -3 ± √13
(3, -21)
x2 + 6x = 7 ⇒ x2 + 6x + 9 = 7 + 9 ⇒ (x + 3)2 = 16 ⇒ x + 3 = ±4 ⇒ x = -7 or 1
x2 + 6x + 1 = 0 x2 + 6x + 9 = 8 (x + 3)2 = 8 x + 3 = ± 2√2 x + 3 = -3 ± 2√2 x ∈ {-3 - 2√2, -3 + 2√2}
y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7
(x - 3)(x - 2)
x2-6x+9 = (x-3)(x-3) when factorised.
x2 +6x = 27 x2 + 6x - 27 = 0 x2 + 9x - 3x - 27 = 0 x(x + 9) - 3(x + 9) =0 (x - 3)(x + 9) = 0 So x can equal 3 or -9.
x²+6x+9=49 x²+6x-40=0 x1=-6/2 - Square root of ((6/2)²+40) x1=-3 - 7 x1= -10 x2=-6/2 + Square root of ((6/2)²+40) x2=-3 + 7 x2= 4
x2 - 6x = 16 ∴ x2 - 6x + 9 = 25 ∴ (x - 3)2 = 25 ∴ x - 3 = 25 ∴ x = 28
20 and the vertex of the parabola is at (3, 20)