College Algebra Unit 2 Test

Front

What is a quadratic function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is a linear function?

Back

A linear function is a polynomial function of degree 1, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How can you identify a function from a graph?

Back

A function can be identified from a graph by using the vertical line test; if a vertical line crosses the graph more than once, it is not a function.

Front

What does it mean if a function is not defined?

Back

A function is not defined at a certain point if there is no output (y-value) for a given input (x-value), often due to division by zero or taking the square root of a negative number.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula (-b/2a, f(-b/2a)).

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

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.