The function g(x) = x² + 5x + 2
Step-by-step explanation:
Let us revise the horizontal translation
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
∵ f(x) = x² - 3x - 2
∵ f(x) is shifted 4 units left
- That means add 4 to each x in the function f(x)
∴ g(x) = (x + 4)² - 3(x + 4) - 2
Simplify it by solving the bracket of power two and open the other
bracket by multiply it by 3 and adding the like terms
∵ (x + 4)² = (x)(x) +2(x)(4) + (4)(4)
∴ (x + 4)² = x² + 8x + 16
∵ 3(x + 4) = 3x + 12
∴ g(x) = [x² + 8x + 16] - [3x + 12] - 2
∴ g(x) = x² + 8x + 16 - 3x - 12 - 2
- Add like terms
∴ g(x) = x² + (8x - 3x) + (16 - 12 - 2)
∴ g(x) = x² + 5x + 2
g(x) = x² + 5x + 2
Learn more:
You can learn more about quadratic function in brainly.com/question/9390381
#LearnwithBrainly
the simplification performed in step 2 is invalid or incorrect
