Question

Please show work on how you got the answer

12.    Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4.  (Your equation must only have integer coefficients, meaning no fractions or decimals.)

13.   Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0.
 
 
14.   Write a quadratic equation that cannot be factored.
 
 
15.   The product of two consecutive positive integers is 72. Find the integers.

Answer 1

Answer: 12) y = 2x² - 7x - 4

13) y = x²

14) y = x² + 3x + 1

15) 8, 9

Explanation:

12)

`x=-(1)/(2)\quad x=4\\\\\\\bigg(x+(1)/(2)\bigg)=0\qquad (x-4)=0`

(2x + 1) = 0 (x - 4) = 0

(2x + 1)(x - 4) = 0

2x² - 7x - 4 = 0

y = 2x² - 7x - 4

13) x = 0 x = 0

(x)(x) = 0

x² = 0

y = x²

14) It is factorable if the sum of two factors of the c-value is the b-value.

One example: x² + 3x + 1 = 0

The only factors of 1 are 1 × 1 → 1 + 1 ≠ 3

So this is not factorable.

15) Let n represent one of the integers, then n + 1 is the other integer.

n(n + 1) = 72

n² + n = 72

n² + n - 72 = 0

(n - 8)(n + 9) = 0

n = 8, n = -9

Since the requirement is that the integer is positive, then n = -9 is not valid.

If n = 8, then n + 1 = 9

Answer: 8, 9