Question

Re-write the quadratic function below in Standard Form y=-5(x+1)²+7

Answer 1

Answer: y = -5x² - 10x + 2

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

`\Large\boxed{y=-5x^2-10x+2}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

y = - 5x² - 10x + 2

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