Question

please help me and explain to me how you got the answer, pls don’t just say the answer explain how. will mark brainliest if you get it right!

Answer 1

Given:

The height of the swipe card in feet after t seconds is

$h(t)=-3t^2+15t+18$

To find:

The maximum height of the swipe card and the time at which it reaches this height.

Solution:

We have,

$h(t)=-3t^2+15t+18$

Here, leading coefficient is -3, which is negative. It means it is a downward parabola and the vertex of the downward parabola is the point of maximum.

If a quadratic function is $f(x)=ax^2+bx+c$, then the vertex is

$Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)$

In the given function, we get

$a=-3,b=15,c=18$

Now,

$-\dfrac{b}{2a}=-\dfrac{15}{2(-3)}$

$-\dfrac{b}{2a}=2.5$

Putting t=2.5 in the given function, we get

$h(2.5)=-3(2.5)^2+15(2.5)+18$

$h(2.5)=36.75$

So, the vertex of the given parabola is at (2.5,36.75).

Therefore, the maximum height of the swipe card is 36.75 feet and it reaches this height after 2.5 seconds.