Answer:
44.1m
Step-by-step explanation:
we are given a quadratic function which represents the height and time of a baseball
[tex] \displaystyle h = 29.4t - 4.9 {t}^{2} [/tex]
we want to figure out maximum height of
the baseball
since the given function is a quadratic function so we have a parabola
which means figuring out the maximum height is the same thing as figuring out the maximum y coordinate (vertex)
to do so we can use some special formulas
recall that,
[tex] \displaystyle \rm t= \frac{ - b}{ 2a} [/tex]
[tex]\displaystyle H_{\text{max}}=f(t)[/tex]
notice that, our given function is not in standard form i.e
[tex] \displaystyle f(x) = a {x}^{2} + bx + c[/tex]
let's make it so
[tex] \displaystyle h = - 4.9 {t}^{2} + 29.4t[/tex]
therefore we got
our a is -4.9 and b is 29.4
so substitute:
[tex] \displaystyle\rm t= \frac{ -( 29.4)}{ 2 \cdot - 4.9} [/tex]
remove parentheses and change its sign:
[tex] \displaystyle\rm t= \frac{ -29.4}{ 2 \cdot - 4.9} [/tex]
simplify multiplication:
[tex] \displaystyle\rm t= \frac{ -29.4}{ - 9.8} [/tex]
simplify division:
[tex] \displaystyle \: t = 3[/tex]
so we have figured out the time when the baseball will reach the maximum height
now we have to figure out the height
to do so
substitute the got value of time to our given function
[tex]\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot {3}^2[/tex]
simplify square:
[tex]\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot 9[/tex]
simplify mutilation:
[tex]\displaystyle H_{\text{max}}=88.2-44.1[/tex]
simplify substraction:
[tex]\displaystyle H_{\text{max}}=44.1[/tex]
hence,
the maximum height of the baseball is 44.1 metres
