A.2+ Converting Between Quadratic Forms

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.

Front

How do you convert a quadratic function from factored form to standard form?

Back

To convert from factored form f(x) = a(x - r1)(x - r2) to standard form, expand the expression using the distributive property.

Front

What is factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the function.

Front

What are the roots of a quadratic function?

Back

The roots of a quadratic function are the values of x that make the function equal to zero.

Front

How do you find the roots of a quadratic equation in standard form?

Back

You can find the roots using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean for a quadratic function to be factorable?

Back

A quadratic function is factorable if it can be expressed as the product of two binomials.

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 distinct real roots; if zero, one real root; if negative, no real roots.

Front

Convert to standard form: f(x) = (x + 7)(x - 3)

Back

f(x) = x² + 4x - 21.

Front

Convert to factored form: f(x) = x² + 3x - 18

Back

f(x) = (x + 6)(x - 3).

Front

Convert to factored form: f(x) = x² + 5x - 24

Back

f(x) = (x + 8)(x - 3).