Question

Which system of equations is represented by the graph?

A. y = x2 − 5x − 3
6x − y = −27

B.y = x2 − 5x + 3
6x − y = 27

C. y = x2 + 5x + 3
6x + y = −27

D. y = x2 + 5x − 3
6x + y = 27

Answer 1

C. y = x2 + 5x + 3
6x + y = −27

Answer 2

The correct option is C.

Explanation:

The vertex form of a parabola is

`y=a(x-h)^2+k` .... (1)

Where, (h,k) is vertex.

From the given figure it is clear that the vertex of the parabola is at (-2.5, -3.25) and the y-intercept is (0,3).

Substitute h=-2.5, k=-3.25, x=0 and y=3 in equation (1) to find the value of a.

`3=a(0+2.5)^2-3.25`

`3+3.25=6.25a`

`6.25=6.25a`

Divide both sides by 6.25.

`1=a`

Substitute h=-2.5, k=-3.25 and a=1 in equation (1), to find the equation of parabola.

`y=1(x+2.5)^2-3.25`

`y=x^2+5x+6.25-3.25`

`y=x^2+5x+3`

The equation of parabola is
`y=x^2+5x+3`.

If a line passes through two points then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The line passes through two points (-6,9) and (-5,3).

`y-9=(3-9)/(-5+6)(x+6)`

`y-9=(-6)/(1)(x+6)`

`y-9=-6(x+6)`

`y-9=-6x-36`

Add 9 on both the sides.

`y=-6x-36+9`

`y=-6x-27`

The equation of line is y=-6x-27.

Therefore the correct option is C.