Quadratic Formula

What does a positive discriminant indicate?

• A positive discriminant indicates that the quadratic equation has two distinct real solutions.

• A positive discriminant indicates that the quadratic equation has one real solution.

• A positive discriminant indicates that the quadratic equation has no real solutions.

• A positive discriminant indicates that the quadratic equation has complex solutions.

What is the relationship between the discriminant and the graph of a quadratic function?

• The discriminant determines the number of x-intercepts (real solutions) of the graph of the quadratic function.

• The discriminant indicates the vertex of the quadratic function.

• The discriminant shows the direction of the parabola (upward or downward).

• The discriminant provides the maximum value of the quadratic function.

What is the formula for the discriminant?

• D = b² - 4ac

• D = 4a - b²c

• D = b² + 4ac

• D = 2b - ac

What is the value of the discriminant for the equation 4x² + 6x - 4 = 0?

• 100

• 64

• 36

• 0

What does the discriminant tell us?

• It indicates the nature of the roots of the quadratic equation.

• It provides the value of the quadratic equation at its vertex.

• It determines the slope of the quadratic function.

• It calculates the area under the quadratic curve.

If a quadratic equation has a discriminant of 28, how many solutions does it have?

• It has 1 real solution.

• It has 2 real solutions.

• It has no real solutions.

• It has infinitely many solutions.

Solve using the Quadratic Formula: x² + 2x + 1 = 0

• x = 1

• x = -1

• x = 0

• x = -2

Calculate the discriminant for the equation x² - 4x + 4 = 0.

• 0, indicating 1 real solution

• 4, indicating 2 real solutions

• -4, indicating no real solutions

• 8, indicating 2 real solutions

How can you determine the number of solutions without solving the equation?

• By calculating the discriminant (D = b² - 4ac) and analyzing its value.

• By graphing the equation and counting the intersections with the x-axis.

• By substituting values into the equation and checking for equality.

• By using the quadratic formula to find the roots.

What does a discriminant of zero indicate?

• A discriminant of zero indicates that the quadratic equation has exactly one real solution (a repeated root).

• A discriminant of zero indicates that the quadratic equation has two distinct real solutions.

• A discriminant of zero indicates that the quadratic equation has no real solutions.

• A discriminant of zero indicates that the quadratic equation has complex solutions.