12/3 Using Factored Form and Standard Form of a Quadratic

Front

What is the factored form of a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is expressed as ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the zero product property state?

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 solve the equation (x + 2)(x - 3) = 0?

Back

Set each factor to zero: x + 2 = 0 or x - 3 = 0. Thus, x = -2 or x = 3.

Front

Convert the factored form (x - 3)(x + 5) to standard form.

Back

The standard form is x^2 + 2x - 15.

Front

What is the value of b in the quadratic function f(x) = 3x^2 + 4x - 5?

Back

The value of b is 4.

Front

How do you find the roots of the quadratic equation x^2 + 9x - 36 = 0?

Back

Factor the equation to (x + 12)(x - 3) = 0, giving roots x = -12 and x = 3.

Front

What is the significance of the coefficients a, b, and c in the standard form of a quadratic equation?

Back

Coefficient a determines the direction of the parabola (upward or downward), b affects the position of the vertex, and c is the y-intercept.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you convert from standard form to vertex form?

Back

Complete the square on the quadratic expression to rewrite it in vertex form.