Answer:
33) 4x² + 8x + 1
35) -2x² + 36x - 147
Explanation:
#33: f(x) = 4(x+1) ² - 3
f(x) = 4(x+1) ² - 3
First Step: Multiply (x+1) (x+1)
(x + 1)² or (x+1)(x+1) is a one real double.
A one real double means that there is only one real solution
(x + 1) (x + 1) = x² + 2x + 1
Second Step: Multiply x² + 2x by 4
4(x² + 2x + 1) = 4x² + 8x + 4
Final Step: Put -3 in the Quadratic Function and do -3 + 4 to get your constant
4x² + 8x - 3 + 4
= 4x² + 8x + 1
#35: f(x) = -2(x - 9) ² + 15
First Step: Multiply (x - 9) (x - 9)
Remember, (x - 9) ² or (x - 9) · (x - 9) is a one real double, meaning that there is only one real solution.
(x - 9) (x - 9) = x² - 18x + 81
Second Step: Multiply by -2
-2 (x² - 18x + 81) = -2x² + 36x - 162
Final Step: Add the constant by 15 in the equation. (Hint: the constant is -162)
-2x² + 36x - 162 + 15
= -2x² + 36x - 147
This is how you convert the function into standard form. Hope this helps.