Answer:
Explanation:
If the discriminant of a quadratic function is 64 and its vertex is in quadrant III, here are three things you can know about the function and/or its graph:
The function has two distinct real roots. The discriminant of a quadratic function is the value under the square root in the quadratic formula:
x = (-b +/- √(b^2 - 4ac)) / 2a
If the discriminant is positive, it means that there are two real roots (values of x that make the equation equal to zero). If the discriminant is negative, it means that there are no real roots (the equation has no solutions). If the discriminant is zero, it means that there is only one real root (the equation has one solution). Therefore, if the discriminant is 64, it means that the function has two distinct real roots.
The graph of the function is a parabola that opens downward. The direction in which a parabola opens (upward or downward) is determined by the coefficient of the x^2 term (a). If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. In this case, the vertex of the parabola is in quadrant III.