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:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
f(x) = x² - 4x + 3
This means that [tex]a = 1, b = -4, c = 3[/tex]
So
[tex]\Delta = b^{2} - 4ac = (-4)^2 - 4(1)(3) = 16 - 12 = 4[/tex]
[tex]x_{1} = \frac{-(-4) + \sqrt{4}}{2} = 3[/tex]
[tex]x_{2} = \frac{-(-4) - \sqrt{4}}{2} = 1[/tex]
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.
