Find the y-coordinate of the vertex of the parabola whose equation is y = x² - x + 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. 

It is given that

y = x² - x + 2

Then, axis of symmetry (x-coordinate of vertex) = -b/2a

Where, a = 1, b = -1

x = - (-1)/2(1)

x = 1/2

Now, substitute the value of x in the given equation to find y - coordinate,

y = (1/2)2 - (1/2) + 2

y = 1/4 - 1/2 + 2

y = 1/4 - 2/4 + 8/4

y = (1 - 2 + 8)/4

y = 7/4

Vertex = (1/2 , 7/4)

Therefore, the y-coordinate of the vertex of the parabola is y - 7/4.

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Find the y-coordinate of the vertex of the parabola whose equation is y = x² - x + 2?

Summary:

The y-coordinate of the vertex of the parabola whose equation is y = x² - x + 2 is y - 7/4.