Question

What is the vertex of the quadratic function f(x) = (x - 3)(x - 2)?

Answer 1

Answer:

$(\frac{5}{2} , -\frac{1}{4} )$

Step-by-step explanation:

Lesson : Finding vertex from quadratic functions ,

Given:

f(x) = (x - 3)(x - 2)

"Vertex"

Find the x intercepts by using the zero product property,

(x - 3)     (x - 2)  =  0

x = 3       x = 2

X-int = (3,0) , (2,0)

Now find the y intercepts by factoring the equation ,

(x - 3)(x - 2)

x * x

x^2

x * -2

x^2 -2x

-3 * x

x^2 -2x -3x

-3 * -2

x^2 -2x -3x + 6

Combining like terms:

x^2 -5x + 6

Replace x with zero,

0^2 -5(0) + 6

6

y intercept = (0,6)

Now graph :

Graph shown

Find vertex -  $(\frac{5}{2} , -\frac{1}{4} )$