The _______ of a quadratic equation can be used to find the number of solutions it has. ??
A. vertex
B. Axis of Symmetry
C. Discriminant
D. Leading Coefficent
Odd q
Odd question. a quadratic always has two solutions, real, or complex.
The vertex can tell you if the solutions are real (sometimes a double solution, if the vertex is on the coordinate), or complex numbers.
The correct answer is C. Discriminant.
To find the number of solutions of a quadratic equation, you can use the discriminant. The discriminant is calculated using the formula:
Discriminant = b^2 - 4ac
where a, b, and c are the coefficients of the quadratic equation (ax^2 + bx + c = 0).
By evaluating the discriminant, you can determine the characteristics of the solutions:
1. If the discriminant is greater than zero (D > 0), then the quadratic equation has two distinct real solutions. This means the equation intersects the x-axis at two different points.
2. If the discriminant is equal to zero (D = 0), then the quadratic equation has one real solution, referred to as a double root. This means the equation touches the x-axis at one point.
3. If the discriminant is less than zero (D < 0), then the quadratic equation has no real solutions. This means the equation does not intersect the x-axis and stays above or below it.
Therefore, by calculating the discriminant, you can determine whether a quadratic equation has zero, one, or two solutions.