How do you use the quadratic formula to solve for x-intercepts #x^2 - 8x + 12 = 0#?

Question

Eva Abramson · Accepted Answer

See a solution process below:

According to the quadratic formula, For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by: #x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))# Replacing: #color(red)(1)# for #color(red)(a)# #color(blue)(-8)# for #color(blue)(b)# #color(green)(12)# for #color(green)(c)# gives: #x = (-color(blue)((-8)) +- sqrt(color(blue)((-8))^2 - (4 * color(red)(1) * color(green)(12))))/(2 * color(red)(1))# #x = (color(blue)(8) +- sqrt(color(blue)(64) - 48))/2# #x = (color(blue)(8) +- sqrt(16))/2# #x = (color(blue)(8) - 4)/2# and #x = (color(blue)(8) + 4)/2# #x = 4/2# and #x = 12/2# #x = 2# and #x = 6#

Hazel Anglin · Answer

undefined To use the quadratic formula to solve for the x-intercepts of $x^2 - 8x + 12 = 0$, first identify the coefficients a, b, and c in the quadratic equation $ax^2 + bx + c = 0$. In this case, $a = 1$, $b = -8$, and $c = 12$. Then, substitute these values into the quadratic formula:

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

Finally, simplify the expression to find the values of x.