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The path of a diver is given by
$ y = - \frac{4}{9} x^2 + \frac{24}{9} + 12 $
where $ y $ is the height (in feet) and $ x $ is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?
16
Algebra
Chapter 2
Polynomial and Rational Functions
Section 1
Quadratic Functions and Models
Quadratic Functions
Complex Numbers
Polynomials
Rational Functions
Missouri State University
Baylor University
Lectures
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So here we have the path of a diver is given by this parable equation. Why is height and feet and X is the horrid on horizontal distance from the diving board? So the diving board, if you plug in X, equals zero, you see that the diving more is twelve feet high, the person jumps off. And then before they come back down, they reached the Vertex, and we want to know the Y values of the vortex. So that's what we're looking for, the K actually here. It's not necessary to do the standard form. You can use the fact that the birth hicks for a proble is always given by the point where this is coming from the standard form or they're just the original form of ah, quadratic. So this is the value that we want here. First, we need to plug in negative B over two A. So in our problem, we can see that B. It's twenty four over nine and we see that a He's negative for over nine ssa plugging this in. I could cancel those minus signs. You could also cancel those nines and I'LL give you twenty for over eight which equals three. So now we want this value here. So just plug in three and four X. And so our function. So you get negative for over nine times three squared, plus twenty for over nine times three and then plus twelve. We could cancel those. Nice. So here we have cancel three. Twenty for over three years. Eight. Tow us. Write this out. We have negative for plus eight. Closed twelve, and that simplifies to sixteen feet. That is the maximum height of the diver.
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