Standard & Factored Form

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 is factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as a(x - p)(x - q), where p and q are the roots of the equation.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the function equal to zero and solve for x.

Front

What is the relationship between the coefficients and the zeros of a quadratic equation?

Back

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

Front

What does it mean for a quadratic to be in factored form?

Back

A quadratic is in factored form when it is expressed as a product of its linear factors.

Front

How do you convert from standard form to factored form?

Back

To convert from standard form to factored form, you can factor the quadratic expression by finding two numbers that multiply to ac and add to b.

Front

What is the vertex form of a quadratic equation?

Back

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

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, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the factored form of x² - 9?

Back

The factored form of x² - 9 is (x - 3)(x + 3).

Front

How do you expand (x - 4)(x + 2)?

Back

To expand (x - 4)(x + 2), use the distributive property: x² - 4x + 2x - 8 = x² - 2x - 8.