Question

Rewrite the following quadratic functions in intercept or factored form. Show your work.

y = 4x^2 - 19x- 5

Answer 1

(4x + 1)(x - 5)

Explanation:

To start, we know that we will get something in the form of (ax + b)(cx + d), or (ac)x^2 + (ad + bc)x + bd. Making some equations, we can see that ac = 4, ad + bc = -19, and bd = -5. Notice that a and c cannot be 2 and 2, as 2d + 2b = -19 cannot be possible because -19 is odd. Therefore, a is 4 and c is 1 (or vice versa). Plug this back in to get 4d + b = -19, and bd = -5. Simple guess and check shows that d = -5 and b = 1, so the answer is (4x + 1)(x - 5).

Answer 2

y = (4x+1)(x-5)

Explanation:

We are given the following the quadratic function and we are to rewrite it in intercept or factored form:

`y = 4x^2 - 19x- 5`

We can factorize the given quadratic function such that when multiplied, the factors give a product of -20 and when added, they give a result of -19.

`y = 4x^2 + x - 20x - 5`

`y=x(4x+1)-5(4x+1)`

`y=(4x+1)(x-5)`

Therefore, the factored form of the given function is y = (4x+1)(x-5).