Which of the following equations is of a parabola with a vertex at (1, 2)?
y = (x - 1)² - 2
y = (x - 1)² + 2
y = (x + 1)² - 2
y = (x + 1)² + 2

Solution:

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed-line.

The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola./p>

The general equation of the parabola is given by

y = a(x - h)² + k

Where, (h, k) is the vertex

Given, vertex of a parabola is (1, 2)

So, a = 1, h = 1 and k = 2

Substituting the values in the equation

y = 1(x - 1)² + 2

y = (x - 1)² + 2

Therefore, the equation of parabola is y = (x - 1)² + 2.

Which of the following equations is of a parabola with a vertex at (1, 2)?

Summary:

The equation of a parabola with a vertex at (1, 2) is y = (x - 1)² + 2.