Choose the correct vertex of the function f(x) = x2 - X + 2.

Question

asked May 3, 2022 107k views

1 Answer

Raduan Santos · Answer 1 · 2022-05-08T04:15:04+0000

Answer:

The vertex of the function is
((1)/(2), (7)/(4))

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

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

It's vertex is the point
(x_(v), y_(v))

In which

x_(v) = -(b)/(2a)

$y_(v) = -(\Delta)/(4a)$

Where

$\Delta = b^2-4ac$

If a<0, the vertex is a maximum point, that is, the maximum value happens at
x_(v) , and it's value is
y_(v) .

f(x) = x² - X + 2.

Quadratic equation with
a = 1, b = -1, c = 2

So

$\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7$

x_(v) = -((-1))/(2) = (1)/(2)

y_(v) = -(-7)/(4) = (7)/(4)

The vertex of the function is
((1)/(2), (7)/(4))