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Na dives into a pool off of a springboard high dive. Her height (in meters above the water), x xx seconds after diving, is modeled by h ( x ) = − 5 ( x + 1 ) ( x − 3 ) h(x)=−5(x+1)(x−3)h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 3, right parenthesis What is the height of Ana above the water at the time of diving?

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Luv2Teach

Answer:

Step-by-step explanation:

What you have here is the factored form of the quadratic

[tex]ax^2+bx+c[/tex]

where a is the term representing the pull of gravity, b is the upwards vertical velocity and c is the initial height.  If we FOIL that out, we get the equation in a form that is easily analyzed for velocity and initial height.

[tex]y=-5x^2+10x+15[/tex]

This tells us that the initial vertical velocity of the dive was 10 m/sec, and that she was 15 meters up at the time of diving.

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