1st Semester Algebra 2 Final Review

Front

Factor the expression: 9x^2 - 64 completely.

Back

(3x - 8)(3x + 8) - This is a difference of squares.

Front

What is the discriminant formula used to determine the number of solutions for a quadratic equation?

Back

The discriminant is given by b^2 - 4ac.

Front

Find the discriminant for the equation: x^2 - 8x + 16 = 0.

Back

The discriminant is 0, indicating 1 real solution.

Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

A negative discriminant indicates 2 imaginary solutions.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

Solve the equation: x^2 + x = -1.

Back

x = \frac{-1 \pm i\sqrt{3}}{2}.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0.

Front

What is the axis of symmetry for the quadratic equation y = ax^2 + bx + c?

Back

The axis of symmetry is given by x = -\frac{b}{2a}.

Front

What is the effect of the coefficient 'a' in the quadratic equation y = ax^2?

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the solution to the equation: x^2 - 4 = 0?

Back

x = 2 or x = -2 (factored as (x - 2)(x + 2) = 0).