Please help asap brainliest if correct only answer if you're 100% sure you're correct Explain the steps necessary to convert a quadratic function in standard form to vertex form.

See Below.

Step-by-step explanation:

To convert a quadratic in standard form to vertex form, we will complete the square.

Let’s say we have a quadratic in standard form:

To start, we will factor the leading coefficient from the first two terms:

Next, we will divide the coefficient of the second term by 2, square it, and then add it to our equation.

Our coefficient of the second term is b/a. b/a divided by 2 is b/2a. And squaring yields b²/4a². So:

Of couse, we will also need to subtract it as well to keep our equation equal.

Since a is being distributed, we will subtract a(b²/4a²) or b²/4a. So:

Finally, we can use the perfect trinomial pattern to factor. So:

And this is vertex form.

Let’s see this with an example. Say we have:

And we want to convert this to vertex form.

As above, factor out the leading coefficient from the first two terms:

Divide the coefficent of the second term by 2 and then square it.

2/2 is 1. 1 squared is still 1.

So, we will add 1 within our parentheses:

Since we added 1 inside, we must subtract 2(1) outside. So:

Now, we can factor. Therefore:

And this is in vertex form.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2