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Which of the following formulas allows you to find the [tex]\(x\)[/tex]-intercepts of a quadratic function?

A. [tex]\(x = -\frac{b}{2a}\)[/tex]
B. [tex]\(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\)[/tex]
C. [tex]\(x = \frac{b \pm \sqrt{b^2-4ac}}{2a}\)[/tex]
D. None of These
E. [tex]\(y = a(x-h)^2 + k\)[/tex]
F. [tex]\(x = \frac{b}{2a}\)[/tex]


Sagot :

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]