Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (b² - 4ac) tell us about the solutions of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if it's positive, there are 2 real solutions; if it's zero, there is 1 real solution; if it's negative, there are 2 imaginary solutions.

Front

Identify a, b, and c in the quadratic equation: x² - 5x + 6.

Back

a = 1, b = -5, c = 6.

Front

How many solutions does the equation x² + 4x + 5 = 0 have?

Back

2 Imaginary Solutions (discriminant is negative).

Front

What is the value of the discriminant for the equation 2x² - 4x + 2 = 0?

Back

The discriminant is 0, indicating 1 real solution.

Front

Solve the quadratic equation: x² - 8x + 16 = 0.

Back

x = 4 (double root).

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the 'a' value in the quadratic equation ax² + bx + c indicate?

Back

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

Front

How do you find the axis of symmetry for a quadratic equation?

Back

The axis of symmetry can be found using the formula x = -b/(2a).

Front

What is the significance of the roots of a quadratic equation?

Back

The roots are the x-values where the graph of the quadratic intersects the x-axis.