Math Problem Statement

y=2(x−1)(x+2) y-intercept

Solution

To find the y-intercept of the function y=2(x1)(x+2)y = 2(x - 1)(x + 2), we need to determine the value of yy when x=0x = 0.

  1. Substitute x=0x = 0 into the equation: y=2(01)(0+2)y = 2(0 - 1)(0 + 2)

  2. Simplify the expression: y=2(1)(2)y = 2(-1)(2) y=2×2=4y = 2 \times -2 = -4

Therefore, the y-intercept is 4-4, or the point (0,4)(0, -4).

Would you like further details on intercepts or have any questions?

Here are some related questions:

  1. What are the x-intercepts of the function y=2(x1)(x+2)y = 2(x - 1)(x + 2)?
  2. How would the graph of y=2(x1)(x+2)y = 2(x - 1)(x + 2) look?
  3. How does changing the coefficient affect the y-intercept?
  4. How do we find intercepts for more complex polynomial functions?
  5. What other points on the graph are easy to calculate manually?

Tip: The y-intercept of any function can be found by substituting x=0x = 0 into the equation and solving for yy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Intercepts

Formulas

y-intercept of a function at x = 0

Theorems

Definition of y-intercept in function graphs

Suitable Grade Level

Grades 8-10