Question

Please help asap brainliest if correct only answer if you're 100% sure you're correct

Answer 1

Answer:

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:

$\displaystyle{f(x)=ax^2+bx+c$

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

$\displaystyle {f(x)=a(x^2+\frac{b}{a}x)+c$

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:

$\displaystyle {f(x)=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})+c$

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:

$\displaystyle {f(x)=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})+c-\frac{b^2}{4a}$

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

$\displaystyle {f(x)=a(x+\frac{b}{2a})^2+\frac{4ac-b^2}{4a}$

And this is vertex form.

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

$f(x)=2x^2+4x-7$

And we want to convert this to vertex form.

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

$f(x)=2(x^2+2x)-7$

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:

$f(x)=2(x^2+2x+1)-7$

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

$f(x)=2(x^2+2x+1)-7-2$

Now, we can factor. Therefore:

$f(x)=2(x+1)^2-9$

And this is in vertex form.

Answer 2

Answer:

A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.

Step-by-step explanation:

its the sample response