The quadratic 3x^2-24x+72 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?

7

Step-by-step explanation:

Quadratic Equation: 3x² - 24x + 72

The form we are to convert the equation to:

3x² - 24x + 72

a(x + b)² + 72

3(x² - 8x + 24)

Step 1

Make the Quadratic equation (x² - 8x) in the bracket factorisable using completing the square method

3( x² - 8x +(- 8/2)²) + 24

3( x² - 8x + 16 = -24 + 16

3( x² - 8x + 16 + 8 = 0)

3( x² - 8x + 16) + 8

3( x² - 4x + 4x + 16) + 8

3( x(x - 4) -4(x - 4) + 8

3((x - 4)(x - 4) )+ 8

3( (x - 4)² + 8

Using this form

a(x + b)² + c

a = 3

b = -4

c = 8

We were asked to add up constants a, b, c

Therefore,

3 +(-4) + 8

= 7

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17