Review: Absolute Value and Quadratic Functions

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What transformation does g(x) = f(x - 3) represent?

Back

f(x) has been translated to the right 3 units.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

How does the value of 'a' in y = ax^2 affect the graph of the parabola?

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. The absolute value of 'a' determines the width of the parabola.

Front

What is the vertex of a parabola in the form y = a(x - h)^2 + k?

Back

The vertex is the point (h, k) where the parabola changes direction.

Front

What does it mean for a function to be vertically stretched by a factor of 2?

Back

The graph of the function is stretched away from the x-axis by a factor of 2, making it narrower.

Front

What is the vertex of the parabola represented by y = 2(x + 5)^2 - 3?

Back

The vertex is (-5, -3).

Front

What is the equation of the absolute value function that has a vertex at (1, 3)?

Back

y = |x - 1| + 3.

Front

How do you identify if a graph opens up or down?

Back

If the coefficient of x^2 is positive, the graph opens up; if it is negative, the graph opens down.

Front

What type of function is y = |x|?

Back

It is an absolute value function.