Quadratic Equations (Graphing and Factoring)

Front

What is a quadratic equation?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

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

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of breaking down a quadratic equation into the product of two binomials.

Front

What are the zeros of a function?

Back

The zeros of a function are the values of x that make the function equal to zero; they are also the x-intercepts of the graph.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

If 'a' (the coefficient of x²) is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.