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

y = 4x^2 - 19x- 5

Respuesta :

1969976289

Answer:

(4x + 1)(x - 5)

Step-by-step 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).

alinakincsem

Answer:

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

Step-by-step explanation:

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

[tex] y = 4x^2 - 19x- 5 [/tex]

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.

[tex] y = 4x^2 + x - 20x - 5 [/tex]

[tex]y=x(4x+1)-5(4x+1)[/tex]

[tex]y=(4x+1)(x-5)[/tex]

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

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