Question

Find the vertex form of: y=2x^2-5x+13

Answer 1

The vertex form of a quadratic function is:

 f(x) = a(x - h)² + k

The coordinate (h, k) represents a parabola's vertex.

In order to convert a quadratic function in standard form to the vertex form, we can complete the square.

y = 2x² - 5x + 13

Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.

y - 13 = 2x² - 5x

Factor out 2 on the right side of the equation.

y - 13 = 2(x² - 2.5x)

Add (b/2)² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2)² by 2 again on the left side.

y - 13 + 2(2.5/2)² = 2(x² - 2.5x + (2.5/2)²)

y - 13 + 3.125 = 2(x² - 2.5x + 1.5625)

Add the constants on the left and factor the expression on the right to a perfect square.

y - 9.875 = 2(x - 1.25)²

Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.

y = 2(x - 1.25)² + 9.875

Vertex: (1.25, 9.875)

Solution: y = 2(x - 1.25)² + 9.875

Or if you prefer fractions

y = 2(x - 5/4)² + 79/8