Convert the equation from vertex form to standard form y=−4(x+5)2−3

Question

Convert the equation from vertex form to standard form  y=−4(x+5)2−3

Responses

y=−4x^2−25x−3

y=16x^2+160x+412

y=−4x^2−40x−103

y=16x^2+160x+397

GPT-4o mini · Answer

To convert the equation $ y = -4(x + 5)^2 - 3 $ from vertex form to standard form, we will first expand the equation. 1. Start with the vertex form: $$ y = -4(x + 5)^2 - 3 $$ 2. Expand $ (x + 5)^2 $: $$ (x + 5)^2 = x^2 + 10x + 25 $$ 3. Substitute this back into the equation: $$ y = -4(x^2 + 10x + 25) - 3 $$ 4. Distribute the $-4$: $$ y = -4x^2 - 40x - 100 - 3 $$ 5. Combine the constant terms: $$ y = -4x^2 - 40x - 103 $$ Thus, the standard form of the equation is: $$ \boxed{y = -4x^2 - 40x - 103} $$ This matches one of the given responses.