Solving Quadratics and Quadratic Formula

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, where a, b, and c are constants and a ≠ 0.

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

What does the discriminant (b² - 4ac) indicate?

Back

The discriminant determines the nature of the roots of a quadratic equation: if > 0, two distinct real roots; if = 0, one real root; if < 0, two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you convert a quadratic equation to standard form?

Back

To convert to standard form, rearrange the equation to the form ax² + bx + c = 0 by moving all terms to one side.

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 using the quadratic formula: n² = 9n - 20

Back

n = 4 and n = 5.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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

Front

Solve using the quadratic formula: 2x² - 9x - 35 = 0

Back

x = -5/2 and x = 7.

Tags

CCSS.HSA-REI.B.4B

Front

Solve using the quadratic formula: x² + 4x - 40 = -8

Back

x = -8 and x = 4.

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.