Question

F(x)=2(x+3)^2-6Now write the above function in standard form and use it to identify the y-intercept.

Answer 1

First let's state the standard form of the quadratic equation:

$y=ax^2+bx+c$

Where c is the y-intercept.

Now, let's put the function F(x) in the standard form:

$\begin{gathered} f(x)=2(x+3)^2-6 \\ f(x)=2(x^2+6x+9)-6 \\ f(x)=2x^2+12x+18-6 \\ f(x)=2x^2+12x+12 \end{gathered}$

Comparing the function with the model, we have c = 12, therefore the y-intercept is equal 12.