Question
An object is thrown into the air graph the situation is in the function y equals negative 4T squared plus 10t what is the maximum height object will reach in feet
Answers
GPT-4o mini
The function given is \( y = -4t^2 + 10t \), which represents the height \( y \) of an object at time \( t \). This is a quadratic function in the standard form \( y = ax^2 + bx + c \), where \( a = -4 \), \( b = 10 \), and \( c = 0 \).
To find the maximum height of the object, we can use the vertex formula for a quadratic function, which occurs at \( t = -\frac{b}{2a} \).
1. Calculate \( t \):
\[
t = -\frac{b}{2a} = -\frac{10}{2 \times -4} = \frac{10}{8} = 1.25 \text{ seconds}
\]
2. Substitute \( t = 1.25 \) into the height function to find the maximum height:
\[
y = -4(1.25)^2 + 10(1.25)
\]
\[
= -4(1.5625) + 12.5
\]
\[
= -6.25 + 12.5
\]
\[
= 6.25 \text{ feet}
\]
Therefore, the maximum height the object will reach is **6.25 feet**.
To find the maximum height of the object, we can use the vertex formula for a quadratic function, which occurs at \( t = -\frac{b}{2a} \).
1. Calculate \( t \):
\[
t = -\frac{b}{2a} = -\frac{10}{2 \times -4} = \frac{10}{8} = 1.25 \text{ seconds}
\]
2. Substitute \( t = 1.25 \) into the height function to find the maximum height:
\[
y = -4(1.25)^2 + 10(1.25)
\]
\[
= -4(1.5625) + 12.5
\]
\[
= -6.25 + 12.5
\]
\[
= 6.25 \text{ feet}
\]
Therefore, the maximum height the object will reach is **6.25 feet**.