The function f(x) = -x2 - 9x + 10 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? x = 1; the diver jumps in the pool at 1 foot per second x = 10; the diver jumps in the pool at 10 feet per second x = 1; the diver hits the water 1 foot away horizontally from the board x = 10; the diver hits the water 10 feet away horizontally from the board I got x = 1 and x = 10 but I still don't know the answer.

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The function f(x) = -x2 - 9x + 10 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? x = 1; the diver jumps in the pool at 1 foot per second x = 10; the diver jumps in the pool at 10 feet per second x = 1; the diver hits the water 1 foot away horizontally from the board x = 10; the diver hits the water 10 feet away horizontally from the board I got x = 1 and x = 10 but I still don't know the answer.

Mathematics
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A zero is the x value which makes the function equal to 0. So it's what we were trying to do in the last problem, find the value of x that makes the function equal to 0. So for f(x) = -x^2 -9x + 10, we would want to factor and solve for x.

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Ok so I would plug in 10 and 1 and see which works? But they both work?
Wait, is it D?
Well, it wouldnt be both, its only x = 1. Would you know how to factor that quadratic?
Umm, no I don't think so. I used the Quadratic formula because I couldn't factor it. :)
Gotta practice your factoring then xD Well, \(-x^{2} - 9x + 10 = 0\) is equivalent to solving \(x^{2} + 9x - 10=0\). I just flipped the signs. To factor this, we want to find factors of -10 that would add up to +9. So when we consider factors of -10, we can come up with 10 and -1. These two numbers work because 10 and -1 multiply to -10 and add to +9. Once we find these two numbers, we can write the quadratic as \((x+10)(x-1)\). Can you see how that works?
Lol ik XD I seriously stink at this. Something to practice over the summer I guess! ;) Yeah, that would make sense :D
I remember this from my lesson now :)
Yeah, definitely. But yes, you would have (x+10)(x-1) = 0. This means we have x+10 = 0 -> x = -10 x-1 = 0 -> x = 1 We ignore the x = -10, though. This is a problem in the physical world. x represents a horizontal distance and distance isn't negative. You don't walk -5 miles, lol. So we only consider the x = 1 option.
But I don't see how I would get an answer from that :|
Well, if youre solving (x+10)(x-1) = 0, the goal is to find an x value that would make the left side = 0. We want to have 0 = 0. Since the left side has two things being multiplied, we can make the left side 0 if either of the multiplied factors is 0. So the easiest thing to do is just set each factor equal to 0. SO thats why I did x+10 = 0 and x-1 = 0
Oh, ok! So would it be C then? :D
Yep :3
Yay! Thanks so much XD you've helped me what two or three times today? Thank you. You've been SO helpful. I wish you could fan someone more than once. I will definitely practice my factoring though, so I don't have to keep taking up your time. Talk to ya later! :D
Lol, yeah, itll be important to get good at that. You always have quadratic formula as a survival method, but practice not needing to rely on that unless necessary, like in the one approximate problem. Good luck :)

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