Review for Quadratics Flashcard (OPTIONAL)

Front

What is a quadratic function?

Back

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

Front

What does it mean to translate a graph up 5 units?

Back

Translating a graph up 5 units means shifting every point on the graph vertically upwards by 5 units.

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 whether it opens upwards or downwards.

Front

How do you identify the direction a parabola opens?

Back

A parabola opens upwards if the coefficient of x² (a) is positive and downwards if a is negative.

Front

What are the roots of a quadratic function?

Back

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

Front

What is the axis of symmetry in a parabola?

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 is the standard form of a quadratic function?

Back

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

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex.

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, calculated using the vertex formula.

Front

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

Back

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