Math Problem Statement

Given g(x) = 3x2 − x + 5, find the following.

(a)

g(0)

Solution

To find g(0)g(0) for the given function g(x)=3x2x+5g(x) = 3x^2 - x + 5, substitute x=0x = 0 into the equation:

g(0)=3(0)20+5g(0) = 3(0)^2 - 0 + 5

g(0)=0+0+5=5g(0) = 0 + 0 + 5 = 5

So, g(0)=5g(0) = 5.

Would you like more details or have any questions?

Here are five related questions for practice:

  1. What is g(1)g(1) for the same function?
  2. How do you find g(2)g(-2) for this function?
  3. If g(x)=0g(x) = 0, what are the possible values of xx?
  4. What is the vertex of the quadratic function g(x)=3x2x+5g(x) = 3x^2 - x + 5?
  5. How does the graph of g(x)=3x2x+5g(x) = 3x^2 - x + 5 compare to the graph of f(x)=x2f(x) = x^2?

Tip: For quadratic functions, the leading coefficient determines how narrow or wide the parabola is.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Substitution

Formulas

g(x) = ax^2 + bx + c
g(x) = 3x^2 − x + 5

Theorems

Substitution method

Suitable Grade Level

Grades 8-10