Question

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

Answer 1

Answer:

The vertex of the function is $(\frac{1}{2}, \frac{7}{4})$

Step-by-step 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

$x_{v} = -\frac{b}{2a}$

$y_{v} = -\frac{\Delta}{4a}$

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

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

$x_{v} = -\frac{(-1)}{2} = \frac{1}{2}$

$y_{v} = -\frac{-7}{4} = \frac{7}{4}$

The vertex of the function is $(\frac{1}{2}, \frac{7}{4})$