Question

Emily realizes that the expression x^2+4x+3 can be written many equivalent ways. Select all the expressions below that are equivalent.

Answer 1

Form 1:

For this case we have the following polynomial:

`x ^ 2 + 4x + 3`

We want to write the polynomial in a different way.

We can, for example, factor the polynomial. We have then:

• 1) Two numbers that are added equal to 4.
• 2) Two numbers that multiplied are equal to 3.

Factoring we have:

`x ^ 2 + 4x + 3 = (x + 1) (x + 3)`

Therefore, an equivalent expression is given by:

`(x + 1) (x + 3)`

Answer:

`(x + 1) (x + 3)`

Form 2:

We now write the equation in the form of vertex.

We have then:

`y = a (x-h) ^ 2 + k`

Where,

(h, k): vertice of the parabola

Therefore, rewrite the equation we have:

`y = (x ^ 2 + 4x + 4) + 3-4`

`y = (x + 2) ^ 2-1`

Answer:

Another equivalent form is the vertex form:

`<strong>y = (x + 2) ^ 2-1</strong>`