F(x) = 2(x + 3)^2 – 6
Find the standard form and the y intercept. Please

f(x) = 2x² + 12x + 12; y-intercept is 12

Step-by-step 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!

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step-by-step explanation:

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