Answer:
y = -3x² - 24 x + 50
Step-by-step explanation:
y - 2 = - 3(x+4)²
y - 2 = -3(x²+8x+16)
y - 2 = -3x² -24x +48
y = -3x² - 24 x + 50
ANSWER
The standard form is
.
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
EXPLANATION
The given function is
[tex]y - 2 = - 3(x + 4)^{2} [/tex]
The standard form is given by
[tex]y =a {x}^{2} + bx + c[/tex]
We expand to obtain:
[tex]y - 2 = - 3( {x}^{2} + 8x + 16)[/tex]
We expand the parenthesis to obtain:
[tex]y - 2 = - 3 {x}^{2} - 24x - 48[/tex]
Group the similar terms to obtain:
[tex]y = - 3 {x}^{2} - 24x - 48 + 2[/tex]
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
The standard form is
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
