Write y= -4x² -16x -14 in vertex form. a) y= -4(x-16)² -14 b) y= 4(x+4)² +2 c) y= -4(x+2)² +2 d) y= (x+2)² -14

Put brackets around the first two terms on the right. y = (-4x^2 - 16x) - 14Pull out the common factor in the first two terms. y = -4(x^2 + 4x) - 14Divide the middle term by 2. Add that inside the brackets. square y = -4(x^2 +4x +(4/2)^2 - 14y = -4(x^2 + 4x + 4) - 14 + 16 This is the step where most people stumble. The point is why is 16 added? It is because what you have done inside the brackets is multiplied 4 by - 4 (on the left). That means you have changed the equation by -16. To counter that, you must add 16 after the - 14. The result is y= -4(x^2 + 4x+4) + 2Express the terms inside the brackets as a square. y =  - 4(x + 2)^2 + 2

B and D are both wrong. B has +4 outside the brackets. It is - 4

D is wrong because there is no 4 of any kind outside the brackets.

A is incorrectly represented inside the brackets as 16. That's not right

That only leaves  C. <<<< Answer

Graphs

Notice that the red parabola and the green one are the same thing.

Red: y = -4x^2 - 16x - 14

Green: y = -4(x + 2)^2 + 2