Math Problem Statement

give me the y intercepts of this graph: g(x)= (x+1) (x-2) (x+5)

Solution

To find the y-intercept of the function g(x)=(x+1)(x2)(x+5)g(x) = (x+1)(x-2)(x+5), we need to evaluate g(0)g(0), since the y-intercept occurs where x=0x = 0.

Let's substitute x=0x = 0 into the equation:

g(0)=(0+1)(02)(0+5)g(0) = (0+1)(0-2)(0+5) g(0)=(1)(2)(5)g(0) = (1)(-2)(5) g(0)=10g(0) = -10

So, the y-intercept is y=10y = -10. Therefore, the point of the y-intercept is (0,10)(0, -10).

Would you like more details on how this is derived, or do you have any other questions? Here are some related questions you might find useful:

  1. How do you factor a cubic function like this one?
  2. What are the roots of the equation g(x)=0g(x) = 0?
  3. How can you graph a cubic function based on its factors?
  4. How do you find the x-intercepts of a polynomial?
  5. What is the general form of a cubic function?

Tip: To quickly find the y-intercept of any function, always set x=0x = 0 and solve for yy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Functions
Intercepts

Formulas

y-intercept: g(0) = f(0)

Theorems

Fundamental Theorem of Algebra

Suitable Grade Level

Grades 9-12