MATH SOLVE

4 months ago

Q:
# Match the parabolas represented by the equations with their vertices.

Accepted Solution

A:

Question asks us to match the list of parabolas, given the vertices.

For any given parabola

f(x)=ax^2+bx+c,the vertex is at x=-b/(2a), and y=-(b^2-4ac)/4a.

This means that given the vertex x=-b/(2a), we just have to compare with -b/2a of each parabola.

For

f1(x)=x^2+6x+8, -b/(2a)=-6/2=-3, so (-3,-1) is a candidate for the vertex.

f2(x)=2x^2+16x+28, -b/(2a)=-16/4=-4, so (-4,-4) is a candidate.

f3(x)=-x^2+5x+14, -b/(2a)=-5/(-2)=2.5, so (2.5,20.25) is a candidate.

f4(x)=-x^2+7x+7, -b/(2a)=-7/(-2)=3.5, so (-3,-1) NO candidate.

f5(x)=2x^2+7x+5, -b/(2a)=-7/4=-1.75, so (-1.75,-1.125) is a candidate, and finally

f6(x)=-2x^2+8x+5, -b/(2a)=-8/(-4)=-2, so (-3,-1) NO candidate.

In principle, we have four candidates for four distinct parabolas, that should be the answer. However, it is better to check the value of f(x) to be sure.

For example,

f1(-3)=-1

f2(-4)=-4

f3(2.5)=20.25

f5(-1)=-1.125

So all candidates check out for the respective functions.

All that is left for you to do is to put the functions in the boxes corresponding to the value of x of the vertex.

For example, place f1(x) in the box corresponding to vertex (-4,-4), etc.)

Sorry, please post the piggy-backed question separately .

For any given parabola

f(x)=ax^2+bx+c,the vertex is at x=-b/(2a), and y=-(b^2-4ac)/4a.

This means that given the vertex x=-b/(2a), we just have to compare with -b/2a of each parabola.

For

f1(x)=x^2+6x+8, -b/(2a)=-6/2=-3, so (-3,-1) is a candidate for the vertex.

f2(x)=2x^2+16x+28, -b/(2a)=-16/4=-4, so (-4,-4) is a candidate.

f3(x)=-x^2+5x+14, -b/(2a)=-5/(-2)=2.5, so (2.5,20.25) is a candidate.

f4(x)=-x^2+7x+7, -b/(2a)=-7/(-2)=3.5, so (-3,-1) NO candidate.

f5(x)=2x^2+7x+5, -b/(2a)=-7/4=-1.75, so (-1.75,-1.125) is a candidate, and finally

f6(x)=-2x^2+8x+5, -b/(2a)=-8/(-4)=-2, so (-3,-1) NO candidate.

In principle, we have four candidates for four distinct parabolas, that should be the answer. However, it is better to check the value of f(x) to be sure.

For example,

f1(-3)=-1

f2(-4)=-4

f3(2.5)=20.25

f5(-1)=-1.125

So all candidates check out for the respective functions.

All that is left for you to do is to put the functions in the boxes corresponding to the value of x of the vertex.

For example, place f1(x) in the box corresponding to vertex (-4,-4), etc.)

Sorry, please post the piggy-backed question separately .