Answer:
The standard form is ⇒ y = -4x² - 32x - 77
Step-by-step explanation:
* Lets look to the vertex form y = a(x - h)² + k
and the standard form y = ax² + bx + c, then equate them
∵ a(x - h)² + k = ax² + bx + c ⇒ solve the bracket
∴ a(x² - 2hx + h²) + k = ax² + bx + c ⇒ open the bracket
∴ ax² -2ahx + ah² + k = ax² + bx + c
* Now lets equate the like terms
∴ a = a ⇒ (1)
∴ -2ah = b ⇒ (2)
∴ ah² + k = c ⇒ (3)
* Lets do the same with the problem
∵ y = -4(x + 4)² - 13
∴ a = -4 , h = -4 , k = -13
* Use (1) , (2) and (3) to find a , b , c
∴ a = -4
∵ b = -2ah
∴ b = -2(-4)(-4) = -32
∵ c = ah² + k
∴ c = (-4)(-4)² + (-13) = -64 + -13 = -77
* Now we can write the standard form y = -4x² - 32x - 77
