Write Quadratics Given the Zeros, A.6C:

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero. They are also known as the x-intercepts of the graph.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) of a quadratic function in standard form y = ax² + bx + c can be found using the formula h = -b/(2a) and k = f(h).

Front

What is 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 convert from standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form, complete the square.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What are the x-intercepts of the quadratic function y = (x - 3)(x + 2)?

Back

The x-intercepts are the values of x that make the function equal to zero: x = 3 and x = -2.

Front

How do you find the quadratic equation given its zeros?

Back

If the zeros are p and q, the quadratic equation can be written as y = a(x - p)(x - q), where 'a' is a non-zero constant.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

What is the formula for the quadratic formula?

Back

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