how do you write this in vertex form?

Question

x²-14.3x-47.32

Answer 1

To put this into vertex form, we will need to "complete the square."

Completing the square uses the coefficient of the 'x' term. It is based on the idea that (x - a) = x^2 - 2ax + a^2.

We are going to create an (x - a)^2 term, and use that to identify the vertex.

In an (x - a)^2 expression, the 'x' term has a coefficient of 2a, we want to divide 14.3 by 2 to find the a we need.

With numbers, it will look like this:

x^2 - 14.3x - 47.32 = (x^2 - 14.3x + (7.15)^2) we got 7.15 by doing 14.3/2

But we haven't dealt with the 47.32 yet, and we just added 7.15^2 to our expression. Adding that extra part will mess things up, so we need to also subtract it. The full expression should now look like this:

x^2 - 14.3x - 47.32 = (x^2 - 14.3x + (7.15)^2) - 47.32 - (7.15)^2

Now we can rewrite the expression as (x - 7.15)^2 - 47.32 - (7.15)^2

Since 7.15^2 = 51.1225 (calculator), we can do some arithmetic.

- 47.32 - (7.15)^2 = - 98.4425.

Putting it all together, we now have:

x^2 - 14.3x - 47.32 = (x - 7.15)^2 - 98.4425

That is vertex form. It shows us that the vertex of the parabola will be at (7.15, -98.4425)

I hope that was clear.

Answer 2

You would want to complete the square in this situation,

Start with (x-a)² & choose a so that you get -14.3x as one of the factors, you do this by taking 14.3/2 = 7.15

So,

(x-7.15)2 = x² -14.3x + 51.1225 So now all we have to do is make the right side equal the original equation

By adding -98.4425 to both sides, we get

(x - 7.15)² -98.4425 = x² - 14.3x + 51.1225 - 98.4425 = x² - 14.3x - 47.32

So the expression on the left is the new vertex form!