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AnnZ [28]
3 years ago
15

The function ƒ is defined by ƒ(x) = (x + 3)(x + 1). The graph of ƒ in the xy-plane is a parabola. Which interval contains the x-

coordinate of the vertex of the graph of ƒ?
Mathematics
1 answer:
Inga [223]3 years ago
5 0

Answer:

All the intervals that contain the number -2 are solution of the problem

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

f(x)=a(x-h)^{2}+k

where

(h,k) is the vertex of the parabola

In this problem we have

f(x)=(x+3)(x+1)

Convert to vertex form

f(x)=x^{2}+x+3x+3

f(x)=x^{2}+4x+3

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-3=x^{2}+4x

Complete the square. Remember to balance the equation by adding the same constants to each side.

f(x)-3+4=x^{2}+4x+4

f(x)+1=x^{2}+4x+4

Rewrite as perfect squares

f(x)+1=(x+2)^2

f(x)=(x+2)^2-1 -------> equation in vertex form

The vertex is the point (-2,-1)

The x-coordinate of the vertex is -2

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