Question

Which form of a quadratic function is easiest to use when finding the maximum or minimum value of the function?

Answer 1

ax² + bx + c

Explanation:

The form of a quadratic equation that is easy to use when finding the maximum or minimum value of the function is ax² + bx + c.

Suppose a quadratic function:

f(x) = 2x² - 8x + 9

Use ( -b/2a , f(-b/2a) ).

-b/2a

a = 2

b = -8

-(-8)/2(2)

8/4

= 2

f(2) = 2(2)² - 8(2) + 9

f(2) = 2(4) - 8(2) + 9

f(2) = 8 - 16 + 9

f(2) = 1

The minimum value of this quadratic function is (2, 1).

It represents a minimum value because a > 0.

Answer 2

Vertex form

Explanation:

There are several forms of the quadratic equation

Standard form: y = ax^2 + bx + c which is useful for the quadratic equation and the axis of symmetry

Factored form: y = (ax - c)(bx - d) which will give us the zeros

and

Vertex form: y = a(x - h)2 + k where ( h,k) is the vertex

The maximum and minimum would be the value of k

It would be maximum when a >0 and minimum when a<0