Compare the functions shown below: f(x) = x3 + 2x2 − 4x − 3

g(x) = polynomial graph with x intercepts at negative 2, negative 1, 1, 3, y intercept at 6

h(x) = trig graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3
Over the interval x = 0 to x = 2π

Which function has the most x-intercepts?

f(x)
g(x)
h(x)
All three functions have the same number of x-intercepts.

9514 1404 393

  g(x)

Step-by-step explanation:

f(x) is cubic, so can have at most 3 x-intercepts.

g(x) has 4 x-intercepts listed.

h(x) has 2 x-intercepts listed.

__

g(x) has the most x-intercepts.

6 (3) - 4 + 32

hope this

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.