What is the vertex form of the equation? Show steps
y=-x^2+12x-4
y = -x^2+12x-4
= -(x^2-12x)-4
= -(x^2-12x+36)-4+36
= -(x-6)^2 + 32
Well, well, well, it seems like you're trying to find the vertex form of that quadratic equation. Let the clown show you some steps with a sprinkle of humor!
First, we need to complete the square. So, let's focus on the quadratic part, -x^2 + 12x. To complete the square, we'll take half of the "x" coefficient, which is 12, and then square it. That gives us (12/2)^2 = 36.
Now, we add and subtract that magical 36 within the parentheses. So, our equation becomes:
y = -(x^2 - 12x + 36 - 36) - 4
Don't worry, this trick doesn't change anything. We're just rearranging the terms a bit.
Next, let's rewrite the quadratic part as a perfect square trinomial:
y = -((x - 6)^2 - 36) - 4
Ah, there you have it! We converted the quadratic part into a beautiful perfect square trinomial, (x - 6)^2. But we can't forget about that -36 and -4 outside of the parentheses.
Let's simplify a bit further:
y = -(x - 6)^2 + 36 - 4
Almost done, my friend! Let's combine those constants:
y = -(x - 6)^2 + 32
Ta-da! We have transformed the equation y = -x^2 + 12x - 4 into vertex form, y = -(x - 6)^2 + 32. The vertex, in this case, is located at (6, 32).
Remember, math can be fun, even if it involves clowning around with quadratic equations!
To find the vertex form of the equation, we can complete the square. The vertex form of a quadratic equation is given by:
y = a(x - h)^2 + k
where (h,k) represents the coordinates of the vertex.
Step 1: Begin with the equation: y = -x^2 + 12x - 4.
Step 2: Take out the common factor from the first two terms by factoring out -1:
y = -(x^2 - 12x) - 4.
Step 3: Now, complete the square by adding and subtracting the square of half the coefficient of the "x" term within the parentheses. In this case, the coefficient of "x" is 12, so we have:
y = -(x^2 - 12x + (12/2)^2) - 4 - (12/2)^2.
y = -(x^2 - 12x + 36) - 4 - 36.
Step 4: Simplify the equation:
y = -(x - 6)^2 - 40.
Hence, the vertex form of the equation y = -x^2 + 12x - 4 is y = -(x - 6)^2 - 40.
y=x^2-12x+38
x^2+12x + 36=4+36
(x+6)^2=40
y=(x+6)^2-40 is vertex form.