Ch 2, 3, & 4 Review CCA 2

Front

What is the sum of the fractions \(\frac{4}{x+3}\) and \(\frac{7}{x+3}\)?

Back

The sum is \(\frac{11}{x+3}\).

Front

What system of linear inequalities is represented by the graph?

Back

The system is \(y \leq 2x - 1\) and \(y > -2x + 3\).

Front

Solve the inequality \((x+4)^2 \leq 36\).

Back

The solution is \(-10 \leq x \leq 2\).

Front

Multiply and simplify the rational expressions \(\frac{(x+3)(x+6)}{x+5} \cdot \frac{x-3}{(x+3)(x-3)}\).

Back

The simplified result is \(\frac{x+6}{x+5}\).

Front

Find the x-intercepts of the quadratic equation \(x^2 - 10x + 21 = 0\).

Back

The x-intercepts are \(x = 7\) and \(x = 3\).

Front

What is the definition of a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are polynomials.

Front

What is the quadratic formula?

Back

The quadratic formula is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) for the equation \(ax^2 + bx + c = 0\).

Front

How do you determine if a quadratic equation has real solutions?

Back

Check the discriminant \(b^2 - 4ac\): if it is positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is the process for factoring a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to \(c\) and add to \(b\) in the expression \(ax^2 + bx + c\).

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points \(x_1\) and \(x_2\) in that interval, if \(x_1 < x_2\), then \(f(x_1) < f(x_2)\).