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Question 57244: 1. A ball follows a flight given by y = 20x - x^2 + 6 where x represents the horizontal distance traveled in feet and y represents the height of the ball in feet. What will be the maximum height of this ball if it is thrown?
2. If x=2, x=-3 and x=0 are zeros of a polynomial, what is a possible equation for this polynomial?
3. What is the vertex of the graph given by
y=2x^2 - 4x + 3? Would the graph be a shift of y=2x^2?
4. Write the equation of the parabola given by y=2x^2-4x+3 in "standard" form.
Thank you very much!!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A ball follows a flight given by y = 20x - x^2 + 6 where x represents the horizontal distance traveled in feet and y represents the height of the ball in feet. What will be the maximum height of this ball if it is thrown?
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Put the equation in the familiar form: y = ax^2+ bx + c
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y = -x^2 + 20x + 6:
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The value of x, at maximum height (y), will occur at the vertex. We can use the vertex formula: x = -b/(2a)
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In your equation: a = -1; b = 20
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x = -20/(2*-1)
x = -20/-2
x = 10 ft is horizontal distance
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To find the max height substitute 5 for x in the orginal equation:
y = 20x - x^2 + 6
y = 20(10) - 10^2 + 6
y = 200 - 100 + 6
y = 106 feet is max height
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2. If x=2, x=-3 and x=0 are zeros of a polynomial, what is a possible equation for this polynomial?
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That would give us factors of (x-2)(x+3) and x
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FOIL the 1st two factors and you have:
x(x^2 + x - 6) = x^3 + x^2 - 6x
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y = x^3 + x^2 - 6x; would give you zeros of -3, 0, and +2
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3. What is the vertex of the graph given by y = 2x^2 - 4x + 3?
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I gave you the vertex formula above. In this equation a = 2, b = -4, since the coefficient of x^2 is positive, there would be a minimum at the vertex
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Would the graph be a shift of y = 2x^2? I would say yes
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4. Write the equation of the parabola given by y = 2x^2-4x+3 in "standard" form. I think that would be: 2x^2 - 4x + 3 = 0
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