Question

The function f of x equals x squared plus 4x plus 3 can be rewritten to reveal the vertex of the parabola in the function notation.



Drag a function and numbers into the blanks to complete the sentence.

Response area with 3 blank spaces
Writing f of x in the equivalent form
Blank space 1 empty
reveals the vertex of the parabola,
which has the coordinates left-parenthesis
Blank space 2 empty
comma
Blank space 3 empty
right-parenthesis.

Answer options with 12 options.

Answer 1

To rewrite the function \( f(x) = x^2 + 4x + 3 \) in vertex form, we can complete the square.

Starting with:
\[
f(x) = x^2 + 4x + 3
\]

We can complete the square:

1. Take half of the coefficient of \( x \) (which is 4), square it:
\[
\left(\frac{4}{2}\right)^2 = 4
\]

2. Rewrite the function:
\[
f(x) = (x^2 + 4x + 4) - 4 + 3 \\
= (x + 2)^2 - 1
\]

Now we have expressed the function in vertex form:
\[
f(x) = (x + 2)^2 - 1
\]

Here, the vertex of the parabola is given by the coordinates \( (-2, -1) \).

Therefore, we can fill in the blanks:

1. Blank space 1: \((x + 2)^2 - 1\)
2. Blank space 2: \(-2\)
3. Blank space 3: \(-1\)

Complete Sentence:

Writing \( f(x) \) in the equivalent form \((x + 2)^2 - 1\) reveals the vertex of the parabola, which has the coordinates \((-2, -1)\).