Respuesta :
a) the maximum height, occurs at the vertex of the quadratic, that is, the U-turn of the parabolic graph, and that occurs at [tex]\bf \qquad \qquad \textit{vertex of a parabola}\\ \quad \\
\begin{array}{lccclll}
y=&\cfrac{-32}{20^2}x^2&+1x&+6\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad \qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so the y-coordinate is the height at that point, or [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex]
b)
when the ball hits the ground the height is 0, because... well, the ball is all the way down, down to the x-axis, at that time y = 0
thus [tex]\bf y=\cfrac{-32}{20^2}x^2+1x+6\implies 0=\cfrac{-32}{20^2}x^2+1x+6[/tex]
solve for "x"
so the y-coordinate is the height at that point, or [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex]
b)
when the ball hits the ground the height is 0, because... well, the ball is all the way down, down to the x-axis, at that time y = 0
thus [tex]\bf y=\cfrac{-32}{20^2}x^2+1x+6\implies 0=\cfrac{-32}{20^2}x^2+1x+6[/tex]
solve for "x"
The maximum height attained by a ball and the horizontal distance traveled at the end of the ball's path which is thrown is required.
The maximum height attained by the ball is 9.125 ft from the ground.
The horizontal distance traveled is 16.93 ft.
The given equation is
[tex]y=-\dfrac{32}{(20)^2}x^2+x+6[/tex]
Since, the equation is of a parabola its vertex x axis point is
[tex]-\dfrac{b}{2a}=-\dfrac{1}{2\times-\dfrac{32}{(20)^2}}=6.25[/tex]
At this point the in the x axis the ball will be at the highest point so,
[tex]y=-\dfrac{32}{(20)^2}\times 6.25^2+6.25+6\\\Rightarrow y=9.125[/tex]
Hence, the maximum height attained by the ball is 9.125 ft from the ground.
At [tex]y=0[/tex] the ball would be on the ground
[tex]0=-\dfrac{32}{(20)^2}x^2+x+6\\\Rightarrow -0.08x^2+x+6=0\\\Rightarrow -8x^2+100x+600=0[/tex]
Solving the equation
[tex]x=\dfrac{-100\pm \sqrt{100^2-4\left(-8\right)\times 600}}{2\left(-8\right)}\\\Rightarrow x=-4.43,16.93[/tex]
The horizontal distance traveled is 16.93 ft.
Learn more:
https://brainly.com/question/10347134
https://brainly.com/question/15642466
