Find table values of this $y=(x-4)(x-2)(x+1)(x+4)$

Question

how to find this $$y=(x-4)(x-2)(x+1)(x+4)$$

I know that x - intercept is $$4,2,-1,-4$$ and y- intercept is $$32$$

In table values $$ x = -5,-3,-1,2,3$$ now What is the values of $y$ ?

Thanks in advance

Plug in your $x$ values? So the value at $x=-1$ is $$(-1-4)(-1-2)(-1+1)(-1+4)=???$$ — Dzoooks, Aug 28 '19 at 02:16
Perhaps you should learn order of operations and learn how to do basic arithmetic. — Dzoooks, Aug 28 '19 at 02:27

score 2 · Accepted Answer · answered Aug 28 '19 at 02:27

Let the function be $f(x)$ for convenience. Plug in each value: $f(-5)=(-5-4)(-5-2)(-5+1)(-5+4)=(-9)(-7)(-4)(-1)=252$

$f(-3)=(-3-4)(-3-2)(-3+1)(-3+4)=(-7)(-5)(-2)(1)=-70$

$f(-1)=(-1-4)(-1-2)(-1+1)(-1+4)=(-5)(-3)(0)(3)=0$

$f(2)=(2-4)(2-2)(2+1)(2+4)=(-2)(0)(3)(6)=0$

$f(3)=(3-4)(3-2)(3+1)(3+4)=(-1)(1)(4)(7)=-28$

BruceET · Answer 2 · 2019-08-28T03:57:18.043

I guess you have what you need in @asdf's Answer (+1), but I wanted to show how to do this sort of thing using R statistical software:

Using R as a calculator:

x = c(−5,−3,−1,2,3)
y = (x−4)*(x−2)*(x+1)*(x+4)
cbind(x,y)
      x   y
[1,] -5 252
[2,] -3 -70
[3,] -1   0
[4,]  2   0
[5,]  3 -28

And to make a plot:

curve((x−4)*(x−2)*(x+1)*(x+4), -7, 6, ylab="y", lwd=2)
 abline(v=c(−5,−3,−1,2,3), col="red")
 abline(h=0, col="green2")

2 Answers2