1st Semester - AA2 Final Review

Front

What does it mean if a zero of a polynomial has even multiplicity?

Back

The graph touches the x-axis at that zero but does not cross it.

Front

What is the discriminant in a quadratic equation and what does it indicate?

Back

The discriminant is given by b² - 4ac. It indicates the nature of the roots: if positive, there are 2 real roots; if zero, 1 real root with multiplicity 2; if negative, 2 imaginary roots.

Front

Convert the equation f(x) = x² - 12x + 40 into vertex form.

Back

f(x) = (x - 6)² + 4.

Front

Simplify the expression (-10 + 6i)/17.

Back

(1 + 50i)/61.

Front

Solve the system of equations: -x + 6y - z = 6, 2x + y - 3z = 16, -x + 5y + 3z = -7.

Back

C (3, 1, -3).

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does it mean for a quadratic function to have imaginary roots?

Back

It means the graph does not intersect the x-axis, indicating no real solutions.

Front

How do you determine the nature of roots using the discriminant?

Back

Calculate b² - 4ac: >0 means 2 real roots, =0 means 1 real root, <0 means 2 imaginary roots.

Front

What is the significance of the turning point in a polynomial function?

Back

It indicates a local maximum or minimum and relates to the multiplicity of the zero.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.