Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Math question can anyone please help?
A person standing close to the edge on top of a 144-foot building throws a baseball vertically upward. The quadratic function models the ball's height above the ground, s(t)= - 16t^2+64t+144, in feet, t seconds after it was thrown. After how many seconds does the ball reach its maximum height? Round to the nearest tenth of a second if necessary.
- JimLv 72 months ago
Quadratic Equation solution for f(x) or y = ax² +bx + c is: x = -b/2a +-√(b² -4ac)/2a (Vertex ± offset)
So t = -b/2a or -64/-32
t = 2.0 sec
If you know calculus, you take 1st differential = 0
slope = 0 for the vertex
- PuzzlingLv 72 months ago
When you have a quadratic, of the form ax² + bx + c, the equation for the line of symmetry is:
x = -b/(2a)
If you need help remembering this, it's the quadratic formula, but without the ±√ part.
In your case the variable is t (time), but its the same thing:
t = -b/(2a)
Plug in your values:
a = -16
b = 64
t = -(64) / (2 * -16)
t = -64/-32
t = 2
That is the vertex of your parabola and since the leading coefficient (a = -16) is negative, the parabola is downward facing. That means the vertex is a maximum.
It reaches its maximum height after 2 seconds.
- PopeLv 72 months ago
s(t) = -16t² + 64t + 144
s(t) = -16(t² - 4t) + 144
s(t) = -16(t² - 4t + 4) + 144 + 16(4)
s(t) = -16(t - 2)² + 208
The maximum height is reached at t - 2 = 0.
t = 2
The baseball reaches a maximum height of 208 feet at two seconds.
- billrussell42Lv 72 months ago
s(t) = –16t² + 64t + 144
diff and set equal to 0 to get max, ie, when v = 0
s' = v = 0 = –32t + 64
t = 2 s