Algebra 2 EOCA Fall Review (Day 2)

Front

What is a quadratic function?

Back

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

Front

How do you find the vertex of a parabola given by a quadratic function?

Back

The vertex of a parabola given by the quadratic function f(x) = ax² + bx + c can be found using the formula: Vertex (h, k) where h = -b/(2a) and k = f(h).

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation ax² + bx + c = 0, and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant, given by D = b² - 4ac, indicates the nature of the roots of the quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root (repeated), and D < 0 means no real roots.

Front

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

Back

A linear function has a constant rate of change and is represented by a straight line (y = mx + b), while a quadratic function has a variable rate of change and is represented by a parabola (y = ax² + bx + c).

Front

How do you complete the square for the quadratic expression x² + 6x + 5?

Back

To complete the square: 1. Take half of the coefficient of x (which is 6), square it (9), and add/subtract it: x² + 6x + 9 - 9 + 5 = (x + 3)² - 4.

Front

What is the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola given by the quadratic function f(x) = ax² + bx + c is the vertical line x = -b/(2a).

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the leading coefficient (a) is positive (a > 0) and opens downwards if the leading coefficient is negative (a < 0).

Front

What is the standard form of a quadratic function?

Back

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

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.