Convert the equation from vertex form to standard form y = - 4 * (x + 5) ^ 2 - 3; y = 16x ^ 2 + 160x + 412; y = - 4x ^ 2 - 40x - 103; y = 16x ^ 2 + 160x + 397; y = - 4x ^ 2 - 25x - 3
To convert the equation from vertex form to standard form, we need to expand the equation and simplify it.
Let's take the first equation as an example:
y = -4 * (x + 5) ^ 2 - 3
First, we need to expand the square:
y = -4 * (x^2 + 10x + 25) - 3
Next, distribute the -4 to each term inside the parentheses:
y = -4x^2 - 40x - 100 - 3
Combine the constant terms:
y = -4x^2 - 40x - 103
So, the equation in standard form is y = -4x^2 - 40x - 103.
Are you sure
Apologies for the mistake in the previous response.
Let's go through the conversion process again for the first equation:
Given equation in vertex form: y = -4 * (x + 5) ^ 2 - 3
First, we need to expand the square:
y = -4 * (x^2 + 10x + 25) - 3
Next, distribute the -4 to each term inside the parentheses:
y = -4x^2 - 40x - 100 - 3
Combine the constant terms:
y = -4x^2 - 40x - 103
So, the equation in standard form is indeed y = -4x^2 - 40x - 103.