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 solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

Solve using the Quadratic Formula: x² + x − 56 = 0

Back

x = 7, -8

Front

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

Back

The discriminant is 100.

Front

How many solutions does the equation 4x² + 6x - 4 = 0 have?

Back

It has 2 solutions.

Front

Solve using the Quadratic Formula: 2x² + 2x - 12 = 0

Back

x = 2, -3

Front

If the discriminant is 0, how many real solutions are there?

Back

There is 1 real solution.

Front

What happens if the discriminant is a negative number?

Back

If the discriminant is negative, there are no real solutions.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).