Question

on a balance beam, one of the leg-moves follows the downward trajectory represented by the equation $x^2 - 8x + 15$. if $x$ represents the number of seconds since the beginning of the leg-move and $y$ represents the distance of the leg from the balance beam, at how many seconds will the leg be on the balance beam? (hint: factor the trinomial, set equal to zero and find the $x$-intercepts.)

Explanation:

Step1: Set equation to 0

When the leg is on the balance beam, $y=0$, so:
$x^2 - 8x + 15 = 0$

Step2: Factor the trinomial

Find two numbers that multiply to 15 and add to -8:
$(x - 3)(x - 5) = 0$

Step3: Solve for x

Set each factor equal to 0:
$x - 3 = 0 \implies x=3$
$x - 5 = 0 \implies x=5$

Answer:

The leg will be on the balance beam at 3 seconds and 5 seconds.