279,376 views
16 votes
16 votes
F(x)= x^2-x rewrite the quadratic function in vertex form and give the vertex

User Kuceb
by
2.8k points

1 Answer

24 votes
24 votes

The vertex form of a quadratic function is expressed as

y = a(x - h)^2 + k

where

h and k are the x and y coordinates of the vertex

a is the leading coefficient(coefficient of the term with the highest exponent)

The standard form of a quadratic function is

f(x) = ax^2 + bx + c

The given function is

f(x)= x^2 - x

By comparing both functions,

a = 1

b = - 1

c = 0

We would calculate the coordinate of the vertex by using the formula

x = - b/2a

x = - - 1/2 * 1 = 1/2

We would find the y coordinate of the vertex by substituting x = 1/2 into the original function. We have

f(1/2) = (1/2)^2 - 1/2 = 1/4 - 1/2 = - 1/4

Thus,

h = 1/2

k = - 1/4

a = 1

The vertex is (1/2, - 1/4)

By substituting these values into the equation, the vertex form is

f(x) = (x - 1/2)^2 - 1/4

User Salient
by
2.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.