That trinomial can't be factored. You would have to complete the square to factor it and even then your answer would be an imaginary number.

x² + x + 12 = 0
x² + x = - 12
x² + x + 1/4 = - 12 + 1/4
x² + x + 1/4 = - 11 3/4
x² + x + 1/4 = - 47/4

(x + 1/2)² = - 47/4
x + 1/2 = +/- √(- 47/4)
x + 1/2 = +/- $\frac{47}{4}i$

x = 1/2 +/- $\frac{47}{4}i$

If the constant was a negative, it would be factor-able (is that a word?).

5 0

4 years ago

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the grap

Studentka2010 [4]

Answer:

D) $(-2,-9)$

Step-by-step explanation:

<u>Vertex Form of a Vertical Parabola:</u>

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

Vertex -> $(h,k)$

Axis of Symmetry -> $x=h$

Vertical Scale Factor -> $a$

To turn $f(x)=x^2+4x-5$ into vertex form, we need to complete the square on the right side
Therefore, if $f(x)=0$ , then $0+9=x^2+4x-5+9$ completes the square on the right side
This becomes $9=(x+2)^2$
This means that our function in vertex form is $f(x)=(x+2)^2-9$

Therefore, the vertex of the graph is $(h,k)=(-2,-9)$ .

3 0

3 years ago