Solving Quadratics - 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: 2x² + 7x - 15 = 0

Back

x = -5 or x = 1.5

Tags

CCSS.HSA-REI.B.4B

Front

Solve: 3a² - 12a + 12 = 0

Back

a = 2

Tags

CCSS.HSA-REI.B.4B

Front

Solve: 9k² = 225

Back

k = -5 or k = 5

Tags

CCSS.8.EE.A.2

Front

What are the x-intercepts of the graph of a quadratic equation?

Back

The x-intercepts are the points where the graph intersects the x-axis, corresponding to the solutions of the quadratic equation.

Tags

CCSS.HSF-IF.C.7A

Front

Solve: 4m² - 100 = 0

Back

m = 5 or m = -5

Tags

CCSS.8.EE.A.2