Solving Quadratics and 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

Identify the values of a, b, and c in the quadratic equation: 4x² - 8x - 3 = 0.

Back

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

Front

Solve by factoring: x² - 9x + 20 = 0.

Back

x = 4 and x = 5.

Front

What is the zero product property?

Back

If the product of two factors is zero, then at least one of the factors must be zero.

Front

Solve using the quadratic formula: 7x² - 26x - 8 = 0.

Back

x = 4 and x = -2/7.

Front

Solve: 2x² + 7x - 15 = 0.

Back

x = -5 and x = 1.5.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0.

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant determines the nature of the roots of a quadratic equation: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you complete the square for the equation x² - 6x + 5 = 0?

Back

Rewrite as (x - 3)² = 4, then solve for x.

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.