Somebody its the last day i dont wanna fail : *( part a: the function f(x) = −x2 − 7x + 30 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. what is a zero of f(x), and what does it represent? part b: solve 9x2 + 3x − 2 = 0 by using an appropriate method. show the steps of your work, and explain why you chose the method used.

Part A. Lest fin the zeros of our function first: 

Step 1. Set the right side of the function equal to 0:


Step 2. Multiply both sides of the equation by -1


Step 3. Factor the left side: 

Step 4. Set each factor equal to 0 and solve for :
and 
and 
Since distances can't be negative, the zero of our function is .
We can conclude that the zero represents that when the horizontal distance of the diver is 3 ft, he is is in the surface of the pool. In other words, his vertical distance is zero. 

Part B. To factor our quadratic equation , we are going to use the method for simple cases because :
Step 1. Find tow numbers whose product is  and its sum is :
We know form our quadratic that , , and , so .
We want tow numbers that multiply together to make -18, and add up to 3.
Those number are 6 and -3.  and 
Step 2. Rewrite the middle term  using those numbers:

Step 3. Factor the expression: