Pandora2016
contestada

Q1. Which system of equations is represented by the graph?

a line is graphed through points negative 6 comma 7 and negative 1 comma 2. It intersects a parabola that opens up at these two points.

A. y = x^2 − 6x − 7
x − y = 1

B. y = x^2 − 6x + 7
x + y = −1

C. y = x^2 + 6x − 7
x − y = 1

D. y = x^2 + 6x + 7
x + y = 1

Q1 Which system of equations is represented by the graph a line is graphed through points negative 6 comma 7 and negative 1 comma 2 It intersects a parabola tha class=

Respuesta :

calculista

Let

[tex] A(-6,7)\\B(-1,2) [/tex]


we know that

The points A and B must satisfy both equations


we proceed to verify each case


case A)

equation [tex] 1 [/tex]

[tex] y=x^{2} -6x-7 [/tex]

check point A

for [tex] x=-6 [/tex]

y must be [tex] 7 [/tex]

substitute

[tex] y=(-6)^{2} -6*(-6)-7 [/tex]

[tex] y=36+36-7\\ y=65 [/tex]

[tex] 65 [/tex] is not equal to [tex] 7 [/tex]

so

The system of equations is not represented by the graph

It is not necessary to check point B


case B)

equation [tex] 1 [/tex]

[tex] y=x^{2} -6x+7 [/tex]

check point A

for [tex] x=-6 [/tex]

y must be [tex] 7 [/tex]

substitute

[tex] y=(-6)^{2} -6*(-6)+7 [/tex]

[tex] y=36+36+7\\ y=79 [/tex]

[tex] 79 [/tex] is not equal to [tex] 7 [/tex]

so

The system of equations is not represented by the graph

It is not necessary to check point B


case C)

equation [tex] 1 [/tex]

[tex] y=x^{2} +6x-7 [/tex]

check point A

for [tex] x=-6 [/tex]

y must be [tex] 7 [/tex]

substitute

[tex] y=(-6)^{2} +6*(-6)-7 [/tex]

[tex] y=36-36-7\\ y=-7 [/tex]

[tex] -7 [/tex] is not equal to [tex] 7 [/tex]

so

The system of equations is not represented by the graph

It is not necessary to check point B


case D)

equation [tex] 1 [/tex]

[tex] y=x^{2} +6x+7 [/tex]

check point A

for [tex] x=-6 [/tex]

y must be [tex] 7 [/tex]

substitute

[tex] y=(-6)^{2} +6*(-6)+7 [/tex]

[tex] y=36-36+7\\ y=7 [/tex]

[tex] 7 [/tex] is equal to [tex] 7 [/tex]------->is ok


check point B

for [tex] x=-1 [/tex]

y must be [tex] 2 [/tex]

substitute

[tex] y=(-1)^{2} +6*(-1)+7 [/tex]

[tex] y=1-6+7\\ y=2 [/tex]

[tex] 2 [/tex] is equal to [tex] 2 [/tex]----->is ok


equation [tex] 2 [/tex]

[tex] x+y=1 [/tex]

check point A

for [tex] x=-6 [/tex]

y must be [tex] 7 [/tex]

substitute

[tex] -6+y=1\\ y=6+1\\ y=7 [/tex]

[tex] 7 [/tex] is equal to [tex] 7 [/tex]------->is ok


check point B

for [tex] x=-1 [/tex]

y must be [tex] 2 [/tex]

substitute

[tex] -1+y=1\\ y=1+1\\ y=2 [/tex]

[tex] 2 [/tex] is equal to [tex] 2 [/tex]----->is ok

therefore


the answer is the option D

[tex] y=x^{2} +6x+7 [/tex]

[tex] x+y=1 [/tex]

Answer:

The correct option is D.

Step-by-step explanation:

From the given graph it is noticed that the line and parabola intersect each other at points (-6,7) and (-1,2). It means each equation of the system must be satisfied by these points.

If a line passing through two points, then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The equation of line is

[tex]y-7=\frac{2-7}{-1-(-6)}(x-(-6))[/tex]

[tex]y-7=-(x+6)[/tex]

[tex]y-7=-x-6[/tex]

[tex]y+x=1[/tex]                        .... (1)

Therefore the equation of line is [tex]y+x=1[/tex].

The standard form of the parabola is

[tex]y=a(x-h)^2+k[/tex]

Where (h,k) is the vertex.

From the graph it is noticed that the vertex of the parabola is (-3,-2).

[tex]y=a(x+3)^2-2[/tex]

The parabola passing through the point (-1,2).

[tex]2=a(-1+3)^2-2[/tex]

[tex]2=4a-2[/tex]

[tex]a=1[/tex]

Therefore the equation of parabola is

[tex]y=(1)(x+3)^2-2=x^2+6x+9-2=x^2+6x+7[/tex]   .... (2)

So, the system of equations contains equation (1) and (2). Option D is correct.

Otras preguntas