LQE (equations & graphs)

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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 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 the base (a positive real number), and x is the exponent.

Front

How can you identify a linear function from a graph?

Back

A linear function will show a straight line when graphed. The slope is constant, and it does not curve.

Front

How can you identify a quadratic function from a graph?

Back

A quadratic function will show a parabolic shape (U-shaped or inverted U-shaped) when graphed.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

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

Back

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

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the rise (change in y) to the run (change in x) between any two points on the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.