a cannonball is shot into the air its height can be described by the equation h=-3t^2+30t-27 where H is the height in feet and t is the time in seconds&nbsp;A) what are the zeros of this relation?&nbsp;B) what do the zeros mean in this situation?&nbsp;C) what is the axis of symmetry and what does it represent?&nbsp;D) What is the vertex and what does it represent in this situation?

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a cannonball is shot into the air its height can be described by the equation h=-3t^2+30t-27 where H is the height in feet and t is the time in seconds&amp;nbsp;A) what are the zeros of this relation?&amp;nbsp;B) what do the zeros mean in this situation?&amp;nbsp;C) what is the axis of symmetry and what does it represent?&amp;nbsp;D) What is the vertex and what does it represent in this situation?

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Solve a cannonball is shot into the air. Its height can be described by the equation h=−3t2+30t−27, where h is the height in feet and t is the time in seconds.A) To find the zeros of this relation, we need to solve the equation h=0. So let&#039;s set h to zero and solve for t:−3t2+30t−27=0To simplify this equation, we can divide every term by 3:t2−10t+9=0Now, we can factor this quadratic equation:(t−1)(t−9)=0Setting each factor to zero, we find the zeros of the relation:t−1=0⟹t=1t−9=0⟹t=9Therefore, the zeros of this relation are t=1 and t=9.B) In this situation, the zeros of the relation represent the times when the height of the cannonball is zero. In other words, they correspond to the moments when the cannonball hits the ground or reaches its initial launch position.C) The axis of symmetry can be found using the formula t=−b2a, where a and b are the coefficients of the quadratic equation in standard form (at2+bt+c=0). In our equation, a=−3 and b=30.t=−302(−3)=−30−6=5Therefore, the axis of symmetry is t=5.In this context, the axis of symmetry represents the time at which the cannonball reaches its maximum height. It divides the parabolic path into two equal halves.D) To find the vertex, we substitute the value of the axis of symmetry (t=5) into the equation for height:h=−3(5)2+30(5)−27h=−3(25)+150−27h=−75+150−27h=48Hence, the vertex of the parabolic path is (5,48), where 5 represents the time in seconds and 48 represents the height in feet.

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