Quadratic Formula

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 = b² - 4ac) indicates the nature of the roots of a quadratic equation: 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.

Front

Identify the values of a, b, and c in the equation: 4x² - 8x = 3.

Back

a = 4, b = -8, c = -3.

Front

How do you find the discriminant of a quadratic equation?

Back

To find the discriminant, use the formula D = b² - 4ac, where a, b, and c are the coefficients from the quadratic equation ax² + bx + c = 0.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Subtract 3 from both sides to set the equation to zero: x² + 6x - 16 = 0.

Front

What are the solutions of the quadratic equation x² + 8x + 16 = 0?

Back

The solutions are x = -4 (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, it means the quadratic equation has no real solutions; the solutions are complex or imaginary.

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 can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

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).