Answer:
The height of the missile in the air after 11 seconds is 330 feet.
Step-by-step explanation:
The standard form for the quadratic function f(x)= , which is the function of the parabola model.
We are given two points.
(1, 130) and (2, 240)
Here the first coordinate represents the x (time) and the second coordinate represents h(x), which is height.
Now plug these two coordinates and find the two equations.
(1, 130), the equation is
130 = a.(1)^2 + b(1) + c, where "c" is the initial height. Which is equal to zero.
Therefore, we get
130 = a + b + 0
a + b = 130 -------(1)
Now let's form the second equation using the coordinate (2, 240)
240 =
240 = 4a + 2b -------------(2)
Now let's solve the equations (1) and (2) and find the value of "a" and "b"
a + b = 130 can be written as a = 130 - b
Here we can use the substitution method.
Now plug in a = 130 - b in the second equation, we get
240 = 4(130 - b) + 2b
240 = 520 - 4b + 2b
240 = 520 - 2b
2b = 520 - 240
2b = 280
Dividing both sides by 2, we get
b = 140
Now plug in b = 140 in a = 130 -b and find the value of a
a = 130 - 140
a = -10
Now we got a = -10 and b = 140.
We plug in a = -10 and b = 140 in the general form, we gety
h(x) =
Where c is the initial height, which is equal to 0.
h(x) =
Now plug in x = 11 seconds and find the height.
h(11) = -10(11)^2 + 140 (11)
= -10 (121) + 1540
= - 1210 + 1540
h(11) = 330 feet,
Therefore, the height of the missile in the air after 11 seconds is 330 feet.