EVA IS JUMPING ON A TRAMPOLINE .HER HEIGHT H AT TIME T CAN BE MODELED BY THE EQUATION H=-16T^2+20T+6.WOULD EVA REACH A HEIGHT OF 14 FEET
To determine if Eva would reach a height of 14 feet, we can substitute H = 14 in the equation H = -16T^2 + 20T + 6 and solve for T.
So, substituting H = 14 into the equation, we have:
14 = -16T^2 + 20T + 6
Rearranging the equation to bring it in the standard quadratic form:
-16T^2 + 20T + 6 - 14 = 0
Simplifying further:
-16T^2 + 20T - 8 = 0
To solve this quadratic equation, we can use the quadratic formula:
T = (-b ± √(b^2 - 4ac)) / (2a)
For the equation -16T^2 + 20T - 8 = 0, the coefficients are:
a = -16
b = 20
c = -8
Now substituting these values into the quadratic formula:
T = (-20 ± √(20^2 - 4(-16)(-8))) / (2(-16))
Simplifying further:
T = (-20 ± √(400 - 512)) / -32
T = (-20 ± √(-112)) / -32
Since the term inside the square root (√(-112)) is negative, there are no real solutions for T. Therefore, Eva would not reach a height of 14 feet.
To determine if Eva would reach a height of 14 feet, we need to substitute the given height value into the equation and solve for the corresponding value of time.
The equation given is:
H = -16T^2 + 20T + 6
To find the time at which Eva reaches a height of 14 feet, we need to set H equal to 14 and solve for T:
14 = -16T^2 + 20T + 6
We rearrange the equation to make it a quadratic equation in standard form:
-16T^2 + 20T + 6 - 14 = 0
-16T^2 + 20T - 8 = 0
Now, we can either solve this equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
T = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = -16, b = 20, and c = -8.
T = (-20 ± √(20^2 - 4(-16)(-8))) / (2 * -16)
T = (-20 ± √(400 - 512)) / -32
T = (-20 ± √(112)) / -32
T = (-20 ± 10.583) / -32
Now, we have two possible solutions for T: one with the plus sign, and one with the minus sign. Let's calculate both:
T1 = (-20 + 10.583) / -32
T1 = -0.371
T2 = (-20 - 10.583) / -32
T2 = 0.941
The solutions for T are T1 = -0.371 and T2 = 0.941.
Since time cannot be negative in this context, we can discard the negative solution.
Therefore, the only valid solution for T is T = 0.941.
Now we have the time at which Eva reaches a height of 14 feet: T = 0.941.
the t of the vertex of your parabola is -b/(2a) = -20/-32 = 5/8
at t = 5/8
h = -16(25/64)+20(5/8) + 6 = 12.25
nope!