Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?

The vertex form of the given parabolic equation is and it can be determine by simplifying and then rewriting the given equation in vertex form of parabola.

Given :

Equation -

The given equation represents a parabola and the vertex form of parabola is given by:

 --- (1)

Now, simplify the given equation as:

 ---- (2)

Now, rewrite the equation (2) in form of equation (1).

Therefore, the vertex form of the given parabolic equation is

For more information, refer the link given below:

link

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

First expand to a quadratic

y=2x^2+14x+25

next divide by the leading coefficient (2), or rather factor out the leading coefficient:

y=2[x^2+7x+12.5]]

Complete squares on the expression inside brackets

y=2[(x+3.5)^2-12.25+12.5]

=2[(x+3.5)^2+0.25]

=2[(x+3.5)^2+0.25]

Distribute:

y=2(x+3.5)^2+0.5

The last line above is the vertex form of the same parabola.

2

step-by-step explanation:

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation: