Answer:
(C) x² - 5x - 14
Step-by-step explanation:
The roots of any quadratic equation will always make the equation equal to 0. So, we can test each equation with the values -2 and 7 to test if both values make the equation 0.
Let's start with A. x² + 5x - 14.
(-2²) + (5 × -2) - 14
4 - 10 - 14 = -20, so we already know that A doesn't work as it doesn't equal 0.
Let's try B. (x+2)² + 7.
(-2+2)² + 7
0² + 7
0+7 = 7, so B doesn't work either.
Let's try C. x² - 5x - 14.
(-2²) - (5×-2) -14
4 + 10 - 14 = 0, ooh we're on to something here! However, for this equation to work, both -2 AND 7 have to work with it. Let's try 7.
(7²) - (5×7) - 14
49 - 35 - 14 = 0, so yes! Both -2 and 7 work for this equation. Therefore, the roots -2 and 7 work for the quadratic function of x² - 5x - 14, C.
Hope this helped!
