S1 Get Well Algebra 2

Front

What is the Zero Product Property?

Back

If the product of two factors is zero, then at least one of the factors must be zero. For example, if \( (x + 2)(x - 3) = 0 \), then either \( x + 2 = 0 \) or \( x - 3 = 0 \).

Front

Solve for x using the Zero Product Property: \( (x + 2)(x - 3) = 0 \)

Back

x = -2 and x = 3

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Front

Find the slope in the equation \( y = 2x + 3 \)

Back

The slope is 2.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope \( m \) is calculated as \( m = \frac{y2 - y1}{x2 - x1} \).

Front

Find the slope between the points (1, 2) and (4, 5).

Back

The slope is \( \frac{5 - 2}{4 - 1} = \frac{3}{3} = 1 \).

Front

What does it mean to 'complete the square'?

Back

Completing the square involves rewriting a quadratic equation in the form \( (x + p)^2 = q \) to make it easier to solve.

Front

Complete the square for the expression \( x^2 + 16x + ____ \)

Back

The completed square is \( x^2 + 16x + 64 \).

Front

What is the product of two complex numbers \( (3 + 8i)(-2 - i) \)?

Back

The product is \( 2 - 19i \).

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers and \( i \) is the imaginary unit.