Answer:
y = - 5x² - 10x + 2
Step-by-step explanation:
y = - 5(x + 1)² + 7 ← expand (x + 1)² using FOIL
= - 5(x² + 2x + 1) + 7 ← distribute parenthesis by - 5
= - 5x² - 10x - 5 + 7 ← collect like terms
= -5x² - 10x + 2 ← in standard form
Answer: y = -5x² - 10x + 2
Step-by-step explanation:
Given quadratic function
y = -5 (x + 1)² + 7
Given requirement
Quadratic Standard Form: y = ax² + bx + c
Simplify the exponents
y = -5 (x + 1) (x + 1) + 7
y = -5 (x² + x + x + 1) + 7
y = -5 (x² + 2x + 1) + 7
Expand the parenthesis by distributive property
y = (-5) · x² + (-5) · 2x + (-5) · 1 + 7
y = -5x² + (-10x) + (-5) + 7
y = -5x² - 10x - 5 + 7
Combine like terms
[tex]\Large\boxed{y=-5x^2-10x+2}[/tex]
Hope this helps!! :)
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