Asked by Blue Berry
An object is thrown into the air. Use GeoGebra to graph the situation using the formula y=−4t2+10t
. What is the maximum height the object will reach in feet?(1 point)
feet
. What is the maximum height the object will reach in feet?(1 point)
feet
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Answered by
GPT 3.5
To graph the situation using the formula y = -4t^2 + 10t, we can use GeoGebra.
1. Open GeoGebra and select the Algebra view.
2. In the Input bar, type "y = -4t^2 + 10t" and press Enter.
3. In the Algebra view, you will see a graph of the equation y = -4t^2 + 10t.
4. To find the maximum height the object will reach, we can look for the vertex of the parabola. The vertex of a parabola in the form y = ax^2 + bx + c is given by (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the equation.
In this case, a = -4 and b = 10, so the x-coordinate of the vertex is -10/(2*-4) = 10/8 = 1.25.
We can substitute this x-coordinate back into the equation to find the y-coordinate: y = -4(1.25)^2 + 10(1.25) = -4(1.5625) + 12.5 = 6.25.
5. Therefore, the object will reach a maximum height of 6.25 feet.
1. Open GeoGebra and select the Algebra view.
2. In the Input bar, type "y = -4t^2 + 10t" and press Enter.
3. In the Algebra view, you will see a graph of the equation y = -4t^2 + 10t.
4. To find the maximum height the object will reach, we can look for the vertex of the parabola. The vertex of a parabola in the form y = ax^2 + bx + c is given by (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the equation.
In this case, a = -4 and b = 10, so the x-coordinate of the vertex is -10/(2*-4) = 10/8 = 1.25.
We can substitute this x-coordinate back into the equation to find the y-coordinate: y = -4(1.25)^2 + 10(1.25) = -4(1.5625) + 12.5 = 6.25.
5. Therefore, the object will reach a maximum height of 6.25 feet.
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