You a Miguel Cervantes de Navas y Colon, captain in the Royal Spanish Army in Seville in the year 1842. Outside your barracks wi
ndow is a stack of cannonballs, as shown in the illustration. On an idle afternoon you decide to calculate the number of cannonballs in the stack. what is the number of cannonballs.
2 answers:
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Seems like it would be
Let's solve this problem. We know the equation of <span>the height of the ball that is:
</span>
<span>
Where x represents </span><span>the horizontal distance in yards the ball has traveled in the air. We know that a distance is always positive, so we conclude that x must be greater or equal than 0, so:
</span>
<span>
The horizontal plane represents the zero of the function, given that there is no possibility for the ball to get negative values, then
is also positive. Finally, from the graph, the appropriate domain is:
</span>
<span>
</span><span>
</span>
</span>
<span>
Where x represents </span><span>the horizontal distance in yards the ball has traveled in the air. We know that a distance is always positive, so we conclude that x must be greater or equal than 0, so:
</span>
The horizontal plane represents the zero of the function, given that there is no possibility for the ball to get negative values, then
</span>
</span><span>
</span>
VERTEX
To determine the vertex (coordinate x) of parabola y = ax² + bx + c, use this following formula
x vertex =
y = x² - 2x - 48
a = 1, b = -2, c = -48
plug in the numbers
x vertex =
x vertex =
x vertex =
x vertex = 1
To find y vertex, substitute the value of x vertex to the parabola equation
y = x² - 2x - 48
y = 1² - 2(1) - 48
y = 1 - 2 - 48
y = -49
The vertex is (1, -49)
X-INTERCEPT
x-intercept located in x axis, that means y = 0. Substitute y = 0 to the parabola equation
x² - 2x - 48 = y
x² - 2x - 48 = 0
(x - 8)(x + 6) = 0
x = 8 or x = -6
The x-intercepts are (8,0) and (-6,0)
The answer is first option
To determine the vertex (coordinate x) of parabola y = ax² + bx + c, use this following formula
x vertex =
y = x² - 2x - 48
a = 1, b = -2, c = -48
plug in the numbers
x vertex =
x vertex =
x vertex =
x vertex = 1
To find y vertex, substitute the value of x vertex to the parabola equation
y = x² - 2x - 48
y = 1² - 2(1) - 48
y = 1 - 2 - 48
y = -49
The vertex is (1, -49)
X-INTERCEPT
x-intercept located in x axis, that means y = 0. Substitute y = 0 to the parabola equation
x² - 2x - 48 = y
x² - 2x - 48 = 0
(x - 8)(x + 6) = 0
x = 8 or x = -6
The x-intercepts are (8,0) and (-6,0)
The answer is first option