Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation. If D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

If the discriminant is positive, how many real solutions does the quadratic equation have?

Back

Two real solutions.

Front

If the discriminant is zero, how many real solutions does the quadratic equation have?

Back

One real solution.

Front

If the discriminant is negative, how many real solutions does the quadratic equation have?

Back

No real solutions.

Front

Calculate the discriminant for the equation: 3x² + 8x = 0.

Back

The discriminant is 64.

Front

What is the discriminant of the equation: x² - 6x + 9 = 0?

Back

The discriminant is 0, indicating 1 solution.

Front

Identify the coefficients in the quadratic equation: y = x² + 5x + 7.

Back

a = 1, b = 5, c = 7.

Front

What is the value of the discriminant for the equation: y = x² + 4x + 4?

Back

The discriminant is 0.

Front

What does a positive discriminant tell us about the graph of a quadratic function?

Back

The graph intersects the x-axis at two points.