Natalie found a tennis ball outside a tennis court. she picked up the ball and threw it over the 12 foot fence into the court. the height of the ball, h, and time t seconds is given by the equation h (t) = - 16^2+18t+5. will she make it over the fence

The equation that gives the height is h (t) = - 16t^2 + 18t + 5, which is a parabola.

You cand find the maximum height from the vertex of the parabola.

Let's find the vertex. I will complete squares:

Start by extractin common factor - 16:

-16t^2 + 18t + 5 = - 16 [t^2 - (18/16) t - 5/16]

I will work with the expression inside the square brackets.

t^2 - (18/16) t - 5/16 = t^2 - (9/8) t - 5/16 =

Completing squares: (t - 9/16) ^2 - (9 / 16) ^2 - 5/16

(t - 9/16) ^2 - 81 / 256 - 5/16 = (t - 9/16) ^2 - 161/256

Now, include add include the factor - 16[ (t - 9/16) ^2 + 161/256 ] =

= - 16 (t - 9/16) ^2 + 161/16

That means that the vertex is 9/16, 161/16

So, the maximum height is 161 / 16 = 10,06, which is lower than the fence.

Answer: She will not make it over the fence.