Each of the points A (-1; 4), B (2; -3) and C (-2; 1) is the vertex of one of

| August 10, 2021 | education

Each of the points A (-1; 4), B (2; -3) and C (-2; 1) is the vertex of one of the parabolas given by the formulas: 1) y = 2x² + 8x + 9 2) y = -x² -2x + 3 3) y = x²-4x + 1

Let’s find the coordinates of the vertices of the given parabolas.

If the parabola is given in the form: y = ax2 + bx + c, then the abscissa of the vertex is found by the formula: x = -b / 2a. The ordinate y can be found by substituting the resulting x value in the parabola equation.

Consider the parabola y = 2x² + 8x + 9.
x = -8 / 2 * 2 = -8 / 4 = -2.

y = 2 * 4 – 8 * 2 + 9 = 8 – 16 + 9 = 1.

The vertex of the parabola has coordinates: (-2; 1), i.e. this is point C.

Consider the parabola y = – x² – 2x + 3.
x = 2 / (-2) * 1 = -1.

y = – 1 + 2 + 3 = 4.

The vertex of the parabola has coordinates: (-1; 4), i.e. this is point A.

Consider the parabola y = x² – 4x + 1.
x = 4/2 * 1 = 2.

y = 4 – 4 * 2 + 1 = 4 – 8 + 1 = -3.

The vertex of the parabola has coordinates: (2; -3), i.e. this is point B.

Answer: A – 2, B – 3, C – 1.



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