Chapter 3 Mid-Chapter Flashcard

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the Zero Product Property?

Back

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you find the roots of a quadratic equation?

Back

To find the roots of a quadratic equation ax² + bx + c = 0, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What are the roots of the equation (2x - 1)(x - 5) = 0?

Back

The roots are x = 1/2 and x = 5.

Front

How do you write a quadratic equation given its roots?

Back

If r1 and r2 are the roots, the quadratic equation can be written as a(x - r1)(x - r2) = 0.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola opens upwards if a > 0 and downwards if a < 0 in the standard form f(x) = ax² + bx + c.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you solve a quadratic equation by completing the square?

Back

To solve by completing the square, rearrange the equation to isolate the constant, then add (b/2)² to both sides and factor the left side.

Front

What is the sum and product of the roots of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.