Question

What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?

Answer 1

`\bf \textit{vertex of a parabola}\\ \quad \\ \begin{array}{llccll} y=&1x^2&+2x&-3\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)`

Answer 2

(-1, -4)

Explanation:

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are numbers.

In the equation

y = x² + 2x - 3

a = 1

b = 2

c = -3

We can calculate the x-coordinate of the vertex (xv) using the following expression.

xv = -b / 2a

xv = -2 / 2.1

xv = -1

We can replace this value in the equation to find the y-coordinate of the vertex (yv).

yv = (-1)² + 2.(-1) - 3

yv = -4

The coordinates of the vertex are (-1, -4).