When a baseball is hit, its height h (in meters) above the ground t seconds after being hit is given byht=−5t2+30t+1Use your GDC to graph the parabola. There are two x-intercepts. Find the coordinates of the leftmost x-intercept.
Question
When a baseball is hit, its height h (in meters) above the ground t seconds after being hit is given byht=−5t2+30t+1Use your GDC to graph the parabola. There are two x-intercepts. Find the coordinates of the leftmost x-intercept.
Solution
The question seems to be incomplete. However, I can guide you on how to find the x-intercepts of a parabola given by the equation h = -5t^2 + 30t + 1.
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Set the equation to zero: -5t^2 + 30t + 1 = 0. This is because the x-intercepts are the values of t for which the height h is zero.
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Solve the quadratic equation for t. You can use the quadratic formula for this: t = [-b ± sqrt(b^2 - 4ac)] / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = -5, b = 30, and c = 1.
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Substitute the values of a, b, and c into the quadratic formula and solve for t. This will give you two solutions, t1 and t2.
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The x-intercepts of the parabola are the points (t1, 0) and (t2, 0). The leftmost x-intercept is the one with the smaller value of t.
Please note that you can use your Graphical Display Calculator (GDC) to graph the parabola and find the x-intercepts. The exact steps to do this will depend on the specific model of your GDC.
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