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.

Front

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

Back

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

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.

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.

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.

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.

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).

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).

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.

Front

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

Back

x² = 8, so x = ±√8 = ±2√2.