Solving quadratics using square roots

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is 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 x² term and then taking the square root of both sides to find the values of x.

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 x² in the equation x² + 4 = 68?

Back

Subtract 4 from both sides to get x² = 64.

Tags

CCSS.8.EE.A.2

Front

What are the solutions to the equation x² = 64?

Back

The solutions are x = ±8.

Tags

CCSS.8.EE.A.2

Front

How do you solve the equation 7x² + 1 = 8 using square roots?

Back

First, subtract 1 from both sides to get 7x² = 7, then divide by 7 to get x² = 1, and finally take the square root to find x = ±1.

Tags

CCSS.HSA-REI.B.4B

Front

What is the solution set for the equation x² = 25?

Back

The solution set is {5, -5}.

Tags

CCSS.8.EE.A.2

Front

How do you solve the equation 5b² - 4 = 41?

Back

Add 4 to both sides to get 5b² = 45, then divide by 5 to get b² = 9, and take the square root to find b = ±3.

Tags

CCSS.8.EE.A.2

Front

What are the solutions to the equation k² - 6 = 43?

Back

The solutions are k = ±7.

Tags

CCSS.8.EE.A.2

Front

What is the importance of the discriminant in solving quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Tags

CCSS.HSA-REI.B.4B