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).

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

x = 4 and x = -2/7.

Tags

CCSS.HSA-REI.B.4B

Front

Solve: 2x² + 7x - 15 = 0.

Back

x = -5 and x = 1.5.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.