Alg 2 - 1st Semester Review

Front

Factor the expression: 4a^2 - 25

Back

(2a + 5)(2a - 5) - This is a difference of squares, which can be factored as (a^2 - b^2) = (a + b)(a - b).

Front

Rewrite the expression with a radical: x^{5/4}

Back

\sqrt[4]{x^5} - This represents the fourth root of x raised to the fifth power.

Front

Solve the equation: 10 = \sqrt{14x + 2}

Back

x = 7 - To solve, square both sides and isolate x.

Front

Simplify the expression: \frac{3x}{2} - \frac{6}{x+5}

Back

\frac{3x^2 + 15x - 12}{2(x + 5)} - Combine the fractions over a common denominator.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

Define a quadratic function.

Back

A function of the form f(x) = ax^2 + bx + c, where a ≠ 0.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is given by D = b^2 - 4ac and determines the nature of the roots.

Front

How do you find the axis of symmetry for a quadratic function?

Back

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

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it passes the horizontal line test, meaning each output is produced by exactly one input.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction \frac{p}{q}, while an irrational number cannot be expressed as a simple fraction.