Question

question 16 of 23
1 point
which part of the quadratic formula is the discriminant?
select the correct response:

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

Explanation:

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). The discriminant is the part under the square root, which is \( b^2 - 4ac \). Among the options, the expression \( \sqrt{b^2 - 4ac} \) has the discriminant (\( b^2 - 4ac \)) under the square root, but the discriminant itself is \( b^2 - 4ac \). Wait, no—wait, the question is which part of the quadratic formula is the discriminant. Wait, the options: the first option is \( \sqrt{b^2 - 4ac} \), but the discriminant is \( b^2 - 4ac \). Wait, maybe the options are presented with the square root, but the discriminant is the radicand? No, wait, no—actually, the discriminant is \( D = b^2 - 4ac \), and in the quadratic formula, the part under the square root is \( \sqrt{D} \), but the discriminant is \( D \). But looking at the options, the first option is \( \sqrt{b^2 - 4ac} \), but maybe the question is considering the part with the square root as including the discriminant? Wait, no—let's recall: the quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). The discriminant is \( b^2 - 4ac \). But among the given options, the first option is \( \sqrt{b^2 - 4ac} \), but maybe the question is using the term "the part" as the expression under the square root? Wait, no—wait, the options:

1. \( \sqrt{b^2 - 4ac} \)
2. \( x = -b \pm \sqrt{b^2 - 4ac} \) (no, that's part of the formula)
3. \( x = \frac{-b}{2a} \) (vertex x-coordinate)
4. \( x = \frac{\sqrt{b^2 - 4ac}}{2a} \) (part of the roots)

Wait, no—wait, the discriminant is \( b^2 - 4ac \), but in the options, the first option is \( \sqrt{b^2 - 4ac} \), which is the square root of the discriminant. But maybe the question is considering the discriminant as the expression under the square root, i.e., \( b^2 - 4ac \), but the first option has \( \sqrt{b^2 - 4ac} \). Wait, maybe the question is phrased as "which part of the quadratic formula is the discriminant"—the discriminant is \( b^2 - 4ac \), but in the options, the first option is \( \sqrt{b^2 - 4ac} \), which is the radical part containing the discriminant. Wait, maybe the answer is the first option? Wait, no—let's check again. The discriminant is \( D = b^2 - 4ac \). In the quadratic formula, the part with the square root is \( \sqrt{D} \), but the discriminant is \( D \). However, among the given options, the first option is \( \sqrt{b^2 - 4ac} \), which is the square root of the discriminant. But maybe the question is using the term "the part" as the expression that includes the discriminant, i.e., the radical expression. So the correct response is the first option: \( \sqrt{b^2 - 4ac} \), because that's the part of the quadratic formula that involves the discriminant (the discriminant is \( b^2 - 4ac \), and this is the square root of it, which is the part that determines the nature of the roots).

Answer:

A. \( \sqrt{b^2 - 4ac} \)