Chapter 9.1, Problem 6BCYP

To determine

To Find:

At what height is the javelin thrown.

Answer to Problem 6BCYP

6 feet

Explanation of Solution

Given Information:

Emilio is competing in the javelin throw.The height of the javelin can be modeled by the equation $y=-16x^2+64x+6$ ,where y represents the height in feet of the javelin after x seconds.

Concept Used :

• Quadratic Functions:
• Quadratic functions are non-linear and are of the form:

  $f(x)=a{x}^2+bx+c;a\ne 0$

This is the standard form of Quadratic function.

• y-intercept = The y coordinate of the point at which the graph intersects y-axis = c

Calculation:

• In the equation $y=-16x^2+64x+6$ ; comparing it with standard form of quadratic equation , we have a = -16 , b = 64 , c = 6 .
• To find the height of javelin initially, we have time = 0 second :

That is , the y-intercept of the quadratic equation.

  $\begin{array}{l}y=-16x^2+64x+6\\ $ y=-16{(0)}^2+64(0)+\mathrm{6....................}[x=0]$y=6\end{array}$

So, initially , the javelin is thrown at a height of 6 feet.