The graph of a quadratic equation that has a positive discriminant is shown in the attachment.
<h3>Further explanation</h3>
The quadratic function has the following general equation:
If x₁ and x₂ are the roots of a function of a quadratic equation, then:
Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using:
<h2>D = b² - 4 a c</h2>
From the value of Discriminant , we know how many solutions the equation has by condition:
- <em>D < 0 → No Real Roots</em>
- <em>D = 0 → One Real Root</em>
- <em>D > 0 → Two Real Roots</em>
Let us tackle the problem.
The graph of a quadratic equation that has a positive discriminant is the one that intersect x-axis at two distinct points.
The graph of a quadratic equation that has a negative discriminant is the one that never intersect x-axis.
The graph of a quadratic equation that has a zero discriminant is the one that intersect x-axis at only one point.
To be clearer, it can be seen in the attached image.
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: College
Subject: Mathematics
Chapter: Quadratic Equations
Keywords: Equation , Line , Variable , Line , Gradient , Point , Quadratic , Intersection