ALG Unit 4C Review - Solving Quadratic Equations (ALL Methods)

Front

What is a quadratic equation?

Back

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

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, using the quadratic formula, completing the square, and graphing.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac and add to b, then rewrite the equation as (px + q)(rx + s) = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

Solve: 16a² - 9 = 0

Back

a = -3/4, 3/4

Tags

CCSS.HSA-REI.B.4B

Front

Solve using the quadratic formula: x² - 3x - 4 = 0

Back

x = 4 and -1

Tags

CCSS.HSA-REI.B.4B

Front

Use the quadratic formula to find the solutions for: 0 = -x² - 5x + 12

Back

x = -6.77 and 1.77

Tags

CCSS.HSA-REI.B.4B

Front

Solve by completing the square: k² − 12k + 23 = 0

Back

k = 6 + √13, 6 - √13

Tags

CCSS.HSA-REI.B.4B

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.