Answer :
Answer:
The equation [tex]f(x)=-16(x-1.5)^2+40[/tex] is used to find the maximum height.
The maximum height of the object is 40 feet at x=1.5.
Step-by-step explanation:
The vertex from of a parabola is
[tex]f(x)=a(x-h)^2+k[/tex] ..... (1)
where, a is constant, (h,k) is vertex.
The object's position at time x is given by
[tex]f(x)=-16x^2+vx+s[/tex]
where, v is initial velocity and s is initial height.
It is given that the initial height of the object is 4 feet and initial velocity is 48 feet per second.
Substitute v=48 and s=4 in the above function.
[tex]f(x)=-16x^2+48x+4[/tex]
Rewrite the above equation in vertex form.
[tex]f(x)=-16(x^2-3x)+4[/tex]
If an expression is [tex]x^2-bx[/tex], then we need to add [tex](\frac{b}{2})^2[/tex] in it to make it perfect square.
In the parenthesis b=3,
[tex](\frac{3}{2})^2=(1.5)^2[/tex]
Add and subtract (1.5)^2 in the parenthesis.
[tex]f(x)=-16(x^2-3x+(1.5)^2-(1.5)^2)+4[/tex]
[tex]f(x)=-16(x^2-3x+(1.5)^2)-16(-(1.5)^2)+4[/tex]
[tex]f(x)=-16(x-1.5)^2+36+4[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]f(x)=-16(x-1.5)^2+40[/tex] .... (2)
The equation [tex]f(x)=-16(x-1.5)^2+40[/tex] is used to find the maximum height.
On comparing (1) and (2), we get
a=-16, h=1.5, k=40
Therefore, the maximum height of the object is 40 feet at x=1.5.
Answer:
f(x) = −16(x − 1.5)2 + 40
Step-by-step explanation:
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