Discriminant/Quadratic Formula PRACTICE

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 tell us about a quadratic equation?

Back

The discriminant (D) is the part of the quadratic formula under the square root: D = b² - 4ac. It indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots (the roots are complex).

Front

How do you identify a, b, and c in the quadratic equation 2x² + 4x - 6 = 0?

Back

In the equation 2x² + 4x - 6 = 0, a = 2, b = 4, and c = -6.

Front

Solve the quadratic equation: x² - 5x + 6 = 0.

Back

The solutions are x = 2 and x = 3.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you convert standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

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 images. It can be found using the formula x = -b/(2a).

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola. If a > 0, the parabola opens upwards and has a minimum; if a < 0, it opens downwards and has a maximum.

Front

Solve the quadratic equation: 3x² + 12x + 12 = 0 using the quadratic formula.

Back

The solutions are x = -2 and x = -2 (a repeated root).

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.