Alg 2 Midterm Review

Front

What is the graph of the function f(x) = |x + 2| - 4?

Back

The graph is a V-shaped graph that opens upwards, shifted left 2 units and down 4 units.

Front

Which point is NOT part of the solution set for a given inequality? (0, 0), (5, 1), (-1, -3), (20, -5)

Back

(-1, -3) is NOT part of the solution set.

Front

How do you find the best fitting quadratic model for a set of data?

Back

Use methods like least squares regression to determine the coefficients of the quadratic equation.

Front

What transformation occurs to the Absolute Value Parent Function f(x) = |x| when it becomes f(x) = |x| + 4?

Back

The graph shifts up 4 units.

Front

What is the inverse of the function f(x) = 3x - 5?

Back

f^-1(x) = (x + 5) / 3.

Front

Define a quadratic function.

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

What is the vertex of a quadratic function in standard form?

Back

The vertex is the point (h, k) where the function reaches its maximum or minimum value, found using the formula h = -b/(2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b^2 - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you determine if a function is one-to-one?

Back

A function is one-to-one if it passes the horizontal line test, meaning no horizontal line intersects the graph more than once.

Front

What is the effect of a negative coefficient in front of an absolute value function?

Back

It reflects the graph across the x-axis.