Q47. - Algebra 2

Question

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by $h\left(t\right)=-16t^2+80t+200$. Interpret the meaning of the y-intercept in the context of this problem.

Step-by-Step Solution

Answer

The meaning of y-intercept is the height from which the object is fired at 0 seconds.   

Step 1. Given Information.

The given function is $h\left(t\right)=-16t^2+80t+200$

Step 2. Use the concept.

The y-intercept is the point where the graph intersects the y-axis.

Consider the function $f\left(x\right)=a{x}^2+bx+c,a\ne 0$, the x-coordinate of vertex is $\frac{-b}{2a}$.

The Graph of $f\left(x\right)=a{x}^2+bx+c,a\ne 0$

• opens up and has a minimum value when $a>0$, and
• opens down and has a maximum value when $a<0$

Step 3. Solution.

In the function $h\left(t\right)=-16t^2+80t+200$, we have $a=-16,b=80,c=200$

So, the y-intercept is given by substituting $t=0$

$\Rightarrow h\left(0\right)=-16{\left(0\right)}^2+80\left(0\right)+200=200$

Which is the height from which the object is fired initially.

So, the meaning of y-intercept is the height from which the object is fired at 0 seconds.