Question

5. Which points are on the graph of the equation - 3x2 + 6y + 5 = -7? Select all that apply. Show all work (A) (-3,6) (B) (-2,0) (C) (0,-2) (D) (8,2)

Answer 1

To solve the exercise, replace the coordinates of the points into the given equation.

If after operating, the result is a true proposition then the point belongs to the graph of the equation.

If after operating, the result is a false statement then the point does not belong to the graph of the equation.

Point (A) (-3,6)

`\begin{gathered} 3x^2+6y+5=-7 \\ 3(-3)^2+6(6)+5=-7 \\ 3\cdot9+36+5=-7 \\ 27+36+5=-7 \\ 65=-7 \\ \text{ False proposition} \end{gathered}`

Therefore, the point is not on the graph of the equation.

Point (B) (-2,0)

`\begin{gathered} 3x^2+6y+5=-7 \\ 3(-2)^2+6(0)+5=-7 \\ 3\cdot4+0+5=-7 \\ 12+5=-7 \\ 17=-7 \\ \text{ False proposition} \end{gathered}`

Therefore, the point is not on the graph of the equation.

Point (C) (0,-2)

`\begin{gathered} 3x^2+6y+5=-7 \\ 3(0)^2+6(-2)+5=-7 \\ 3\cdot0-12+5=-7 \\ 0-12+5=-7 \\ -7=-7 \\ \text{ True proposition} \end{gathered}`

Therefore, the point is on the graph of the equation.

Point (D) (8,2)

`\begin{gathered} 3x^2+6y+5=-7 \\ 3(8)^2+6(2)+5=-7 \\ 3\cdot64+12+5=-7 \\ 192+12+5=-7 \\ 209=-7 \\ \text{ False proposition} \end{gathered}`

Therefore, the point is not on the graph of the equation.

Finally, the only point that is on the graph of the equation is point C.

Graphically