Math Problem Statement

Evaluate the following functions: 1. f(x) = 2x + 11 for x = 10. 2. f(x) = -2x^2 + 4x - 7 for x = 2. 3. f(x) = 3x^2 + 5x - 1 for x = 2. 4. f(x) = 2k_2 + 5k_1 + 1 for k_1 = 1 and k_2 = 2.

Solution

The image contains several functions and prompts to evaluate them at specific values of xx. I'll break them down step-by-step for you:

Functions and Evaluation Points:

  1. f(x)=2x+11f(x) = 2x + 11, evaluate for x=10x = 10.
  2. f(x)=2x2+4x7f(x) = -2x^2 + 4x - 7, evaluate for x=2x = 2.
  3. f(x)=3x2+5x1f(x) = 3x^2 + 5x - 1, evaluate for x=2x = 2.
  4. f(x)=2k2+5k1+1f(x) = 2k_2 + 5k_1 + 1, evaluate for k1=1k_1 = 1 and k2=2k_2 = 2.

Let me calculate the values of each function for the given xx and kk values.

1. f(x)=2x+11f(x) = 2x + 11, for x=10x = 10:

f(10)=2(10)+11=20+11=31f(10) = 2(10) + 11 = 20 + 11 = 31

2. f(x)=2x2+4x7f(x) = -2x^2 + 4x - 7, for x=2x = 2:

f(2)=2(22)+4(2)7=2(4)+87=8+87=7f(2) = -2(2^2) + 4(2) - 7 = -2(4) + 8 - 7 = -8 + 8 - 7 = -7

3. f(x)=3x2+5x1f(x) = 3x^2 + 5x - 1, for x=2x = 2:

f(2)=3(22)+5(2)1=3(4)+101=12+101=21f(2) = 3(2^2) + 5(2) - 1 = 3(4) + 10 - 1 = 12 + 10 - 1 = 21

4. f(x)=2k2+5k1+1f(x) = 2k_2 + 5k_1 + 1, for k1=1k_1 = 1 and k2=2k_2 = 2:

f(k1,k2)=2(2)+5(1)+1=4+5+1=10f(k_1, k_2) = 2(2) + 5(1) + 1 = 4 + 5 + 1 = 10

These are the evaluated results for each function. Let me know if you need further clarification or have any additional questions!

Here are 5 related questions to further explore:

  1. What is the derivative of each function?
  2. How would you evaluate f(x)=3x2+5x1f(x) = 3x^2 + 5x - 1 for x=2x = -2?
  3. Can you plot the function f(x)=2x2+4x7f(x) = -2x^2 + 4x - 7 for a range of xx?
  4. How does the evaluation change if you substitute x=1x = -1 in f(x)=2x+11f(x) = 2x + 11?
  5. What are the roots of the quadratic function f(x)=3x2+5x1f(x) = 3x^2 + 5x - 1?

Tip: When dealing with quadratic functions, always remember the formula for finding the roots: x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Evaluating functions
Quadratic functions

Formulas

f(x) = 2x + 11
f(x) = -2x^2 + 4x - 7
f(x) = 3x^2 + 5x - 1
f(x) = 2k_2 + 5k_1 + 1

Theorems

Substitution method for function evaluation

Suitable Grade Level

Grade 7-9