Converting Between Vertex Form and Standard Form

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form f(x) = a(x - h)² + k to standard form, expand the equation: f(x) = a(x² - 2hx + h²) + k = ax² - 2ahx + (ah² + k).

Front

What is the standard form of a quadratic function?

Back

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

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

How do you find the vertex from standard form?

Back

To find the vertex from standard form f(x) = ax² + bx + c, use the formula: h = -b/(2a) and then substitute h back into the function to find k.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form f(x) = ax² + bx + c into vertex form by adding and subtracting (b/2a)².

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set f(x) = 0 and solve the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) 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 convert from standard form to factored form?

Back

To convert from standard form to factored form, you can use factoring techniques or the quadratic formula to find the roots and express the function as f(x) = a(x - r1)(x - r2).