Question

Which is the graph of the function: f(x) = x2 - 4x + 3​

Answer 1

Answer:

Option 1

Step-by-step explanation:

To find the graph of the quadratic function, we find it's zeros.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$.

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$, given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

f(x) = x² - 4x + 3​

This means that $a = 1, b = -4, c = 3$

So

$\Delta = b^{2} - 4ac = (-4)^2 - 4(1)(3) = 16 - 12 = 4$

$x_{1} = \frac{-(-4) + \sqrt{4}}{2} = 3$

$x_{2} = \frac{-(-4) - \sqrt{4}}{2} = 1$

Zeros at x = 1 and x = 3, that is, it crosses the x-axis at this values, so the graph is given by option 1.