Question

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

Answer 1

`((5)/(2) , -(1)/(4) )`

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 -
`((5)/(2) , -(1)/(4) )`