Math Problem Statement

Find the y-intercept of the function f(x) = 2x^2 + 6x - 8

Solution

To find the y-intercept of the function f(x)=2x2+6x8f(x) = 2x^2 + 6x - 8, we need to determine the value of f(x)f(x) when x=0x = 0.

  1. Substitute x=0x = 0 into the function: f(0)=2(0)2+6(0)8=8f(0) = 2(0)^2 + 6(0) - 8 = -8

  2. The y-intercept is the point where x=0x = 0, so the y-intercept is: (0,8)(0, -8)

Thus, the correct answer is:

  • (0,8)(0, -8)

Would you like more details or have any further questions?

Here are some related questions to explore:

  1. How do you find the x-intercepts of a quadratic function?
  2. What is the vertex of this quadratic function?
  3. How can you determine if the parabola opens upwards or downwards?
  4. How do you find the axis of symmetry for a quadratic function?
  5. What are the maximum and minimum values of a quadratic function?

Tip: For any polynomial function, the y-intercept is found by setting x=0x = 0 and solving for f(0)f(0).

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Intercepts

Formulas

f(x) = ax^2 + bx + c
y-intercept occurs at (0, f(0))

Theorems

None

Suitable Grade Level

Grades 8-10