Question

2. Given the quadratic function p(x) = 2x2 - 2x + 5 , find the range values when the domain is

{-2,0,1,5} Write your answer in set notation.

Answer 1

Let's plug the values into the equation:

`\begin{array}cx&f(x)=2x^2-2x+5&\text{value}\\-2&2(-2)^2-2\cdot(-2)+5&17\\0&2(0)^2-2\cdot 0 + 5&5\\1&2(1)^2-2\cdot 1 + 5&5\\5&2(5)^2-2\cdot 5 + 5&45\end{array}`

So, the range is the set composed by the numbers

`\{5,\ 17,\ 45\}`

Answer 2

{ 5, 17, 45 }

Explanation:

To find the range substitute the values from the domain into p(x)

p(- 2) = 2(- 2)² - 2(- 2) + 5 = 2(4) + 4 + 5 = 8 + 4 + 5 = 17

p(0) = 2(0)² - 2(0) + 5 = 0 + 0 + 5 = 5

p(1) = 2(1)² - 2(1) + 5 = 2 - 2 + 5 = 5

p(5) = 2(5)² - 2(5) + 5 = 2(25) - 10 + 5 = 50 - 10 + 5 = 45

Range is { 5, 17, 45 } ← note 5 is only entered once