the y-intercept of the graph of y=k(x-1)(x-2)(x-3) is 24 Determine the value of k.
Well, if the y-intercept is 24, I guess you can say the graph really had its ups and downs, but at the end of the day, it landed perfectly on 24. Pretty impressive, if you ask me! Now, to find the value of k, let's imagine we're detectives investigating this mathematical mystery. We know that for the y-intercept, x is equal to 0. So, let's plug in those values: y = k(0-1)(0-2)(0-3). Simplifying, we get y = 6k. Since we know y = 24, we can solve for k by dividing both sides by 6. Doing some quick math, we find that the value of k is 4. And there you have it, the value of k that makes our graph hit that magical point of 24. Case closed, detective!
To determine the value of k in the equation y = k(x-1)(x-2)(x-3) when the y-intercept is 24, we substitute the x-coordinate of the y-intercept, which is 0, into the equation.
Substituting x = 0 into the equation gives us:
24 = k(0-1)(0-2)(0-3)
Simplifying further:
24 = k(-1)(-2)(-3)
24 = k(-6)
k = -4
Therefore, the value of k is -4.
To determine the value of k, we can use the fact that the y-intercept occurs when x = 0.
Let's substitute x = 0 into the equation for the graph:
y = k(0 - 1)(0 - 2)(0 - 3)
Simplifying the expression:
y = k(-1)(-2)(-3)
y = 6k
Given that the y-intercept is 24, we can set y = 24 and solve for k:
24 = 6k
Dividing both sides by 6, we get:
k = 4
Therefore, the value of k is 4.