Answer:
f(x) = 2x² + 12x + 12; y-intercept is 12
Explanation:
f(x) = 2(x + 3)² - 6
This equation is in point slope form. We want to put it in standard form.
According to PEMDAS (parentheses/exponents | multiplication/division | addition/ subtraction), we should solve the exponent first. (the expression in the parentheses is as simplified as possible).
(x + 3)² → (x +3)(x + 3)
To solve this, we need to FOIL (first | outer | inner | last)
F: x²
O: 3x
I: 3x
L: 9
Combine these terms.
x² + 3x + 3x + 9
x² + 6x + 9
Plug this expression back into your original equation.
f(x) = 2(x + 3)² – 6 → f(x) = 2(x² + 6x + 9) - 6
Next, we will distribute the 2 across the parentheses.
f(x) = 2x² + 12x + 18 - 6
Then, combine like terms. (18 & 6)
f(x) = 2x² + 12x + 12
This is your equation in standard form.
Now we want to find the y-intercept. The y-intercept is the y-value when x = 0. Therefore, we need to plug in x = 0 to the equation.
f(x) = 2x² + 12x + 12
f(x) = 2(0)² + 12(0) + 12
Follow PEMDAS again.
[exponents] → f(x) = 2(0) + 12(0) + 12
[multiplication] → f(x) = 0 + 0 + 12
[addition] → f(x) = 12
Your y-intercept is 12.
Hope this helps!