Solving Quadratics

Front

What is the square root property in solving quadratics?

Back

If ax^2 = c, then x = ±√(c/a). This property allows us to solve quadratic equations by taking the square root of both sides.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve the equation 4m² - 100 = 0?

Back

Using the square root property: 4m² = 100, m² = 25, so m = ±5.

Tags

CCSS.HSA-REI.B.4B

Front

What is the zero product property?

Back

If a*b = 0, then either a = 0 or b = 0. This property is used to solve quadratic equations that are factored.

Tags

CCSS.HSA-REI.B.4B

Front

Is Suzie correct in her solution of x² + 4x - 12 = 2?

Back

No, she factored correctly but cannot use the zero product property as shown because the equation was not set to zero.

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the zeros of a quadratic function?

Back

Set the quadratic equation to zero and solve for x using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-REI.B.4B

Front

What are the steps to solve x² = 16 using the square root property?

Back

1. Isolate x²: x² = 16. 2. Take the square root: x = ±√16. 3. Solutions are x = ±4.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean for a quadratic to have no real solutions?

Back

It means that the quadratic does not intersect the x-axis, often indicated by a negative discriminant (b² - 4ac < 0).

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is b² - 4ac. It determines the nature of the roots: positive (two real solutions), zero (one real solution), or negative (no real solutions).

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic by factoring?

Back

1. Write the quadratic in standard form. 2. Factor the quadratic expression. 3. Set each factor to zero and solve for x.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions to the equation x² - 8 = 0?

Back

x² = 8, so x = ±√8 = ±2√2.

Tags

CCSS.HSA-REI.B.4B