Solve Quadratic Equations using Square Roots

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 does it mean to solve a quadratic equation using square roots?

Back

Solving a quadratic equation using square roots involves isolating the squared term and then taking the square root of both sides to find the variable's values.

Tags

CCSS.HSA-REI.B.4B

Front

What is the square root property?

Back

The square root property states that if x² = k, then x = ±√k.

Tags

CCSS.HSA-REI.B.4B

Front

How do you isolate a squared term in a quadratic equation?

Back

To isolate a squared term, you first move all other terms to the opposite side of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

Solve: (x + 4)² = 36

Back

x = 2, -10

Tags

CCSS.HSA-REI.B.4B

Front

What is the first step in solving 2(w + 1)² = 72?

Back

Divide both sides by 2 to isolate the squared term: (w + 1)² = 36.

Tags

CCSS.HSA-REI.B.4B

Front

Solve: 3x² = 12

Back

x = ±2.

Tags

CCSS.8.EE.A.2

Front

What are complex numbers?

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed as a + bi, where i is the imaginary unit.

Tags

CCSS.HSN.CN.A.1

Front

Solve for y: 3y² - 4 = 287

Back

y = √97, -√97.

Tags

CCSS.8.EE.A.2

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

Tags

CCSS.HSA-REI.B.4B