To find the [tex]\( x \)[/tex]-intercepts of a quadratic function, you should use the quadratic formula. The [tex]\( x \)[/tex]-intercepts occur where the quadratic function [tex]\( f(x) = ax^2 + bx + c \)[/tex] is equal to zero.
Therefore, you need to solve the equation [tex]\( ax^2 + bx + c = 0 \)[/tex] for [tex]\( x \)[/tex]. The quadratic formula used for this purpose is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
This formula provides the solutions for [tex]\( x \)[/tex] which are the points where the quadratic graph intersects the [tex]\( x \)[/tex]-axis.
Now, let's review the given options:
1. [tex]\( x = -\frac{b}{2a} \)[/tex]
2. [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]
3. [tex]\( x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]
4. None of These
5. [tex]\( y = a(x-h)^2 + k \)[/tex]
6. [tex]\( x = \frac{b}{2a} \)[/tex]
The correct formula for finding the [tex]\( x \)[/tex]-intercepts is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Hence, the correct answer is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
