Algebra II Test 6 Review

Front

What is the distance formula in a coordinate plane?

Back

The distance between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

Calculate the distance between the points (-5, -8) and (-1, -16).

Back

Using the distance formula: d = √((-1 - (-5))² + (-16 - (-8))²) = √(4² + (-8)²) = √(16 + 64) = √80 = 8.9 (rounded to the nearest tenth).

Front

What is the product of two functions f(x) and g(x)?

Back

The product of two functions f(x) and g(x) is defined as (f * g)(x) = f(x) * g(x).

Front

If f(x) = x + 5 and g(x) = x² - 2x + 3, what is f(x) * g(x)?

Back

f(x) * g(x) = (x + 5)(x² - 2x + 3) = x³ + 3x² - 7x + 15.

Front

What is the formula to find the distance between two points in a coordinate plane?

Back

d = √((x2 - x1)² + (y2 - y1)²).

Front

Calculate the distance between the points (-5, 3) and (4, -5).

Back

Using the distance formula: d = √((4 - (-5))² + (-5 - 3)²) = √(9² + (-8)²) = √(81 + 64) = √145.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a ≠ 0.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation ax² + bx + c = 0. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A ≥ 0.