Math Problem Statement

find the function of g(x)=x²+2x-2 of x is 1.5

Solution

To find the value of the function g(x)=x2+2x2g(x) = x^2 + 2x - 2 at x=1.5x = 1.5, we substitute x=1.5x = 1.5 into the function.

g(1.5)=(1.5)2+2(1.5)2g(1.5) = (1.5)^2 + 2(1.5) - 2

Let's calculate it step by step:

  1. Calculate (1.5)2(1.5)^2: (1.5)2=2.25(1.5)^2 = 2.25

  2. Calculate 2×1.52 \times 1.5: 2×1.5=32 \times 1.5 = 3

  3. Combine these results: g(1.5)=2.25+32g(1.5) = 2.25 + 3 - 2

  4. Simplify: g(1.5)=2.25+32=3.25g(1.5) = 2.25 + 3 - 2 = 3.25

So, the value of g(1.5)g(1.5) is 3.253.25.

Do you have any questions or would you like more details?

Here are some related questions for further exploration:

  1. What is the derivative of g(x)=x2+2x2g(x) = x^2 + 2x - 2?
  2. Find the value of g(x)g(x) when x=1x = -1.
  3. Determine the roots of the function g(x)=x2+2x2g(x) = x^2 + 2x - 2.
  4. What is the vertex of the parabola represented by g(x)=x2+2x2g(x) = x^2 + 2x - 2?
  5. How does the function g(x)g(x) behave as xx approaches infinity?
  6. Calculate the integral of g(x)g(x) with respect to xx.
  7. Find the second derivative of g(x)=x2+2x2g(x) = x^2 + 2x - 2.
  8. Determine the axis of symmetry for the function g(x)=x2+2x2g(x) = x^2 + 2x - 2.

Tip: When solving polynomial functions, it's helpful to break down each step and simplify incrementally to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions

Formulas

Quadratic function formula g(x) = x^2 + bx + c

Theorems

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Suitable Grade Level

Grades 9-12