h(t)=-4.9t^2+30.5t+8.5
Are you treating to find the roots?
If so use the quadratic formula
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The given expression is h(t) = -4.9t^2 + 30.5t + 8.5. It represents a quadratic function, where h(t) represents the height (or position) at a given time t. To find specific information about the function, let's break down the different elements of the equation.
The equation is in the form of h(t) = at^2 + bt + c, where:
- a represents the coefficient of the quadratic term,
- b represents the coefficient of the linear term,
- c represents the constant term.
In this equation, we have:
- a = -4.9,
- b = 30.5,
- c = 8.5.
This information allows us to interpret various properties of the quadratic function.
1. Vertex: The vertex is the point where the graph of the quadratic function reaches its maximum or minimum value. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a). By substituting the values of a and b into the formula, we get x = -30.5 / (2 * -4.9), which simplifies to x = 3.122. To find the y-coordinate of the vertex, substitute the value of x back into the equation: h(3.122) = -4.9(3.122)^2 + 30.5(3.122) + 8.5.
2. Axis of Symmetry: The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. It passes through the vertex of the parabola. The equation of the axis of symmetry is given by x = -b / (2a). In this case, the axis of symmetry is x = 3.122.
3. Roots (or the x-intercepts): The roots are the values of t where the quadratic function intersects the x-axis. To find the roots, set h(t) = 0 and solve the quadratic equation -4.9t^2 + 30.5t + 8.5 = 0. This can be done using factoring, completing the square, or using the quadratic formula.
4. Maximum or Minimum Value: The minimum or maximum value of the quadratic function can be determined based on the sign of the coefficient of the quadratic term, a. If a is positive, the parabola opens upward, and the vertex represents the minimum value of the function. If a is negative, the parabola opens downward, and the vertex represents the maximum value of the function.
By applying these concepts and calculations, you can obtain specific information about the given quadratic function h(t) = -4.9t^2 + 30.5t + 8.5.