Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots of the equation.

Front

What does a positive discriminant indicate about the solutions of a quadratic equation?

Back

A positive discriminant indicates that there are two distinct real solutions.

Front

What does a discriminant of zero indicate about the solutions of a quadratic equation?

Back

A discriminant of zero indicates that there is exactly one real solution, also known as a repeated or double root.

Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

A negative discriminant indicates that there are no real solutions, but two complex (imaginary) solutions.

Front

How can you calculate the discriminant of the quadratic equation 2x² + 3x - 5 = 0?

Back

The discriminant is calculated as b² - 4ac = (3)² - 4(2)(-5) = 9 + 40 = 49.

Front

If the discriminant of a quadratic equation is negative, what can be said about its graph?

Back

The graph of the quadratic equation does not intersect the x-axis.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, represented by the value of the function when x = 0.

Front

How does the value of 'a' in a quadratic equation ax² + bx + c affect the graph?

Back

The value of 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens, and can be found using the coordinates (h, k) where h = -b/(2a) and k is the function value at h.