y=2x^2-3x write in vertex form

Question

Write the equation in vertex form. Identify the vertex.

 

Answer 1

The equation is y = 2x² - 3x.

Here x² coefficient is 2, for perfect square make x² coefficient 1 by factor out 2.

y = 2(x² - 3/2 x )

To change the expression (x² - 3/2 x ) into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

Here x coefficient = 3/2. so, (half the x coefficient)² = (3/4)²= 9/16.

Add 2(9/16) = 9/8 to each side of the equation.

y + 9/8 = 2(x² - 3/2 x + 9/16)

y + 9/8 = 2(x - 3/4)²

y  = 2(x - 3/4)² - 9/8

The above equation represent the standard form of the equation of parabola.

The standard form of the parabola with vertex (h, k) and axis of symmetry x = h is y = a(x - h)² + k.

The vertex form of the equation of parabola is y  = 2(x - 3/4)² - 9/8 and Vertex : (h, k ) = (3/4, - 9/8).