A2- Module 1 Topic 3 Retest

Front

What is the inverse of the function P(x) = 2x^2 + 1?

Back

P^{-1}(x) = \sqrt{\frac{x-1}{2}}

Front

Is the point (2, 3) part of the solution set for y < 2x^2 - 3x + 1?

Back

No

Front

What are the inverse points for the coordinates (3, 0), (2, -4), (5, 5), and (-6, 8)?

Back

(0, 3), (-4, 2), (5, 5), (8, -6)

Front

What does it mean for a function to have an inverse?

Back

A function has an inverse if each output is produced by exactly one input, allowing us to 'reverse' the function.

Front

What is the definition of a function's inverse?

Back

The inverse of a function f(x) is a function f^{-1}(x) such that f(f^{-1}(x)) = x for all x in the domain of f.

Front

How do you find the inverse of a quadratic function?

Back

To find the inverse of a quadratic function, solve for x in terms of y, then swap x and y.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What is the relationship between a function and its inverse in terms of coordinates?

Back

If (a, b) is a point on the function f, then (b, a) is a point on its inverse f^{-1}.

Front

What does the focus of a parabola represent?

Back

The focus is a point from which distances to points on the parabola are measured, and it is p units away from the vertex.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c, where a, b, and c are constants.