Quadratics

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

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

Back

In vertex form, y = a(x-h)² + k, the vertex is (h, k).

Front

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

Back

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

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 formula x = -b/(2a).

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the x-values where the graph intersects the x-axis, also known as the roots or solutions.

Front

How can you determine the number of solutions a quadratic equation has?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac): if D > 0, there are 2 solutions; D = 0, 1 solution; D < 0, no solutions.

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 is the significance of the discriminant in a quadratic equation?

Back

The discriminant indicates the nature of the roots: positive for two real solutions, zero for one real solution, and negative for no real solutions.