Question

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

Answer 1

Option 1

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\\eq0`.

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) = (-b + √(\Delta))/(2*a)`

`x_(2) = (-b - √(\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) = (-(-4) + √(4))/(2) = 3`

`x_(2) = (-(-4) - √(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.