Question

What is the value of k? with a= 4 and b= -7​

Answer 1

k= -7/4

Step-by-step explanation:

y=ax^2+3x+b, a=4 b=-7

y=4x^2+3x-7

where y=0 at the intersection

4x^2+3x-7=0

by using factorisation method

product=-28

sum=3

factors=7,-4

(4x^2-4x)+(7x-7)=0

4x(x-1)+7(x-1)=0

(4x+7)(x-1)=0

4x+7=0, x-1=0

x=-7/4, x=1

therefore, k= -7/4

Answer 2

The value of k ⇨
`-(121)/(16)`

Step-by-step explanation:

⟺ Substitute a = 4 and b = -7 in the equation.

From
`y=ax^2+3x+b`

Our new equation is
`y=4x^2+3x-7`

⟺ Use the formula of finding k value.

`k=(4ac-b^2)/(4a)\\`

⟺ Substitute a = 4 b = 3 and c = -7 in the formula. (Arranged Expression)

`k=(4(4)(-7)-(3)^2)/(4(4))\\k=(-112-9)/(16)\\k=-(121)/(16)\\`

If you are curious where k-value/term comes form, it comes from this equation.

`y=a(x-h)^2+k`