Question

What is the standard form of `y= (x+3) (x+4)`?

Answer 1

`y=x^2+7x+12`

Explanation:

the standard form of a second-degree polynomial function should look like this

`color(green)(y=ax^2+bx+c`

so we try to reach that for with your function

`y=(x+3)(x+4)`

Using the Distributive property

`y=x(x+4)+3(x+4)`

`y=x*x+x*4+3*x+3*4`

Multiply

`y=x^2+4x+3x+12`

Add like terms

`y=x^2+7x+12`

Answer 2

`x^2 + 7x + 12`

Explanation:

`y = (x+3)(x+4)`

The standard form of a quadratic equation is `ax^2 + bx + c`. To make this equation in standard form, we expand/simplify this using FOIL:

Following this image, we can multiply it out.

The `color(teal)("firsts")`:
`color(teal)(x*x) = x^2`

The `color(indigo)("outers")`:
`color(indigo)(x * 4) = 4x`

The `color(peru)"inners"`:
`color(peru)(3 * x) = 3x`

The `color(olivedrab)"lasts"`:
`color(olivedrab)(3 * 4) = 12`

Combine them all together to get:
`x^2 + 4x + 3x + 12`

We can still combine the like terms `color(blue)(4x)` and `color(blue)(3x)`:
`x^2 + 7x + 12`

As you can see, this matches the form `ax^2 + bx + c`. Therefore, the quadratic equation in standard form is `x^2 + 7x + 12`.

Hope this helps!

Answer 3

`y=x^2+7x+12`

Explanation:

`"the standard form of a quadratic is "`

`•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0`

`"expanding the factors gives"`

`y=x^2+7x+12larrcolor(red)"in standard form"`