Find the vertex of the quadratic function:
y=1/2x^2 + 8x – 50

definition  

The vertex form of a quadratic function is given by

f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.

FYI: Different textbooks have different interpretations of the reference "standard form" of a quadratic function. Some say f (x) = ax2 + bx + c is "standard form", while others say that f (x) = a(x - h)2 + k is "standard form". To avoid confusion, this site will not refer to either as "standard form", but will reference f (x) = a(x - h)2 + k as "vertex form" and will reference f(x) = ax2 + bx + c by its full statement.

When written in "vertex form":

• (h, k) is the vertex of the parabola, and x = h is the axis of symmetry.

• the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0).

• the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

• notice that the h value is subtracted in this form, and that the k value is added.

            If the equation is y = 2(x - 1)2 + 5, the value of h is 1, and k is 5.

            If the equation is y = 3(x + 4)2 - 6, the value of h is -4, and k is -6.

divider

button To Convert from f (x) = ax2 + bx + c Form to Vertex Form:

Method 1: Completing the Square

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example.

example Convert y = 2x2 - 4x + 5 into vertex form, and stat

Step-by-step explanation:

step-by-step explanation:

12475909

the answer would be a 24

step-by-step explanation:

c=2πr=2·π·3=24