h(t)=-4.9t^2+9.8t+39.2 Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water seconds after the throw can be modeled by the quadratic function given. How many seconds after the throw does the stone hit the water?

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h(t)=-4.9t^2+9.8t+39.2 Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water     seconds after the throw can be modeled by the quadratic function given. How many seconds after the throw does the stone hit the water?

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Given height function: We are given the height function h(t) = -4.9t^2 + 9.8t + 39.2, which models the height of the stone above the water in meters t seconds after it is thrown. To find out when the stone hits the water, we need to find the value of t when h(t) = 0.Set height function equal: Set the height function equal to zero and solve for t: 0 = -4.9t^2 + 9.8t + 39.2 This is a quadratic equation in the standard form of at^2 + bt + c = 0, where a = -4.9, b = 9.8, and c = 39.2.Use quadratic formula: To solve the quadratic equation, we can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a) First, we calculate the discriminant (b^2 - 4ac).Calculate discriminant: Calculate the discriminant: Discriminant = b^2 - 4ac Discriminant = (9.8)^2 - 4(-4.9)(39.2) Discriminant = 96.04 - 4(-4.9)(39.2) Discriminant = 96.04 + 768.32 Discriminant = 864.36Plug values into formula: Now that we have the discriminant, we can plug it into the quadratic formula along with the values for a and b: t = (-9.8 ± √864.36) / (2 * -4.9)Calculate two possible values: Calculate the two possible values for t: t = (-9.8 ± √864.36) / (-9.8) t = (-9.8 ± 29.4) / (-9.8) We have two possible solutions for t: t = (-9.8 + 29.4) / (-9.8) or t = (-9.8 - 29.4) / (-9.8)Discard negative solution: Calculate the first possible value for t: t = (-9.8 + 29.4) / (-9.8) t = 19.6 / (-9.8) t = -2 Since time cannot be negative in this context, we discard this solution.Calculate positive value: Calculate the second possible value for t: t = (-9.8 - 29.4) / (-9.8) t = -39.2 / (-9.8) t = 4 This is the positive value for t, which represents the time in seconds when the stone hits the water.

$h(t)=-4.9t^2+9.8t+39.2$ Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water seconds after the throw can be modeled by the quadratic function given. How many seconds after the throw does the stone hit the water?

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