Question

Determine the corresponding general form of each of the following vertex form

Answer 1

Answer:

Step-by-step explanation:

(a + b)² =a² + 2ab + b²

(a -b)² = a² - 2ab + b²

1) y = (x -1)²

 y= x² -  2*x*1 + 1

y = x² - 2x + 1    

Ans: C

2)y = (x +4)² + 5

y = x² +2*x*4 + 4² + 5

  = x² + 8x + 16 + 5

y = x² + 8x + 21

C

3) y = -(x + 9)²- 10

y = - [x² + 18x + 81] - 10

= -x² - 18x - 81 - 10

y =-x² - 18x - 91

B

4) y = 3(x + 2)² - 18

y =3 [x² + 4x + 4] - 18

y =  3x² + 12x  + 12 - 18

y =3x²  + 12x - 6

A

5) y = -2(x + 1)² - 16

       = -2[x² + 2x + 1] -16

       = -2x² - 4x - 2 - 16

     y = -2x² - 4x -  18

A

6) y = 5(x + 5)²

        =5[x²+ 10x + 25]

y = 5x² +50x + 125

A

7)y = (1/2)(x + 8)² - 8

  y = (1/2) (x² + 16x + 64) - 8

$y = \dfrac{1}{2}*x^{2}+ \dfrac{1}{2}*16x + \dfrac{1}{2}*64 -8\\\\\\y =\dfrac{1}{2}x^{2}+8x +32 - 8\\\\\\y=\dfrac{1}{2}x^{2} +8x + 24$

A

8) y = (x + 3/2)² + 3/4

$y = x^{2} +2*x*\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{3}{4}\\\\y=x^{2}+3x+\dfrac{12}{4}\\\\\\y=x^{2}+3x + 3$

C

9) y = 2[x² + 16x + 64] - 5x

y = 2x² + 32x + 64 - 5x

y =2x² + 27x + 6