I forgot how to solve this grade 11 review package question
5) A graph representing the vertical height in metres after t seconds, has been modelled by the equation f(t)= -4.9t^2+6t+0.5.
a) how long is the ball in the air?
b) when does the ball reach its maximum height?
c) what is the maximum height?
*** If you can even provide a website that has similar solutions, it would be very helpful, THANK YOU SOO MUCH!!***
To solve these questions, we need to analyze the given equation, f(t) = -4.9t^2 + 6t + 0.5, which represents the vertical height of a ball after t seconds.
a) To find out how long the ball is in the air, we need to consider the time interval where the ball's height is greater than zero. In other words, we need to find the values of t where f(t) > 0.
To do this, we set the equation equal to zero:
-4.9t^2 + 6t + 0.5 = 0
Then, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Once we find the values of t that satisfy the equation, we can determine the time interval during which the ball is in the air.
b) To find when the ball reaches its maximum height, we need to find the vertex of the parabolic curve, represented by the equation. The vertex is the highest point on the curve, which represents the maximum height of the ball.
The t-value of the vertex can be found using the formula t = -b / (2a), where a, b, and c are the coefficients in the quadratic equation (ax^2 + bx + c = 0). In this case, the equation is -4.9t^2 + 6t + 0.5, so a = -4.9, b = 6, and c = 0.5. By substituting these values into the formula, we can find the t-value for the vertex.
c) To determine the maximum height, we can substitute the t-value of the vertex into the equation f(t) = -4.9t^2 + 6t + 0.5. This will give us the corresponding height at the peak of the parabolic curve.
For more detailed explanations and examples, you may refer to websites that provide tutorials on quadratic equations, such as Khan Academy (www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations-and-inequalities). Additionally, textbooks or review packages for grade 11 math can offer step-by-step solutions and examples for similar problems. Good luck with your review!