Question

I need help with these algebra 2 questions.

1. What is the vertex form of the equation?
y=-x^2+12x-4

2. What is the expression in factored form?
2x^2+16x+24

Answer 1

Factored Form
To do this all you need to do is this

First reorder the terms to look like this :)
\(24 ~+ ~16x ~+~ 2x^2\)

Next you factor out the greatest common factor of 24, 16, and 2, and that is 2, so divide them all by 2

\(24/2 ~+ ~16x/2 ~+~ 2x^2/2\)
\(2(12 ~+ ~8 ~+~ x^2)\)

Now we have \(2(12 ~+ ~8x ~+~ x^2)\), so next we factor a trinomial (a polynomial with three terms)

\(2((6 ~+ ~x)(2 ~+~ x))\)

And take away the extra parenthesis and you have \(2(x~+~6)(x~+~2)\)

Answer 2

Sorry I can't help with the first one

Answer 3

\[y = -x^2 + 12x - 4\]
--------------------
Vertex form is given by the equation
\[y = a(x-h)^2 + k\]
--------------------
\[y = -x^2 + 12x - 4\]
group through parenthesis
\[y = (-x^2 + 12x) - 4\]
factor out -1
\[y = -1(x^2 - 12x) - 4\]
Complete the square by adding and subtracting 36 on the right side of the equation
\[y = -1(x^2 - 12x+36) - 4 + 36\]
Notice that what you'll see are all positive 36 since when you try to distribute -1 outside the quantity it would give you -36
\[y = -1(x-6)^2 +32\]

Answer 4

Thank you both for helping, I really appreciate it. :)