U3: L1-4 Quadratic and Cubic Functions Review

Front

What is a quadratic function?

Back

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

Front

What does the coefficient 'a' in a quadratic function determine?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards (minimum point); if 'a' is negative, it opens downwards (maximum point).

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or 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 is the standard form of a cubic function?

Back

The standard form of a cubic function is f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is the difference between a quadratic function and a cubic function?

Back

A quadratic function has a degree of 2 and produces a parabola, while a cubic function has a degree of 3 and produces an S-shaped curve.

Front

What does it mean to find the inverse of a function?

Back

Finding the inverse of a function means switching the x and y values, effectively reflecting the graph over the line y = x.

Front

How do you find the inverse of the function f(x) = 7(x + 4)²?

Back

1. Divide by 7; 2. Take the square root of the quantity; 3. Subtract 4.

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, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is a maximum point in a quadratic function?

Back

A maximum point is the highest point on the graph of a quadratic function that opens downwards.