Sample 1: A rectangle has a perimeter of 170 centimeters and a length of 60 centimeters. Find the area.

Solution: Let be the length andbe the height. Then

That means that, or equivalently, we get. That implies that the area

is

Sample 2: When using the quadratic formula to solve a quadratic equation (ax² + bx + c = 0), the discriminant is b² - 4ac. This discriminant can be positive, zero, or negative.

Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax² + bx + c.

Solution:

• Let’s consider the equation:

For this equation, the discriminant is:

This means that the graph of the equationcrosses twice theaxis.

• Let’s consider the equation:

For this equation, the discriminant is:

This means that the graph of the equationtouches only once theaxis.

• Let’s consider the equation:

For this equation, the discriminant is:

This means that the graph of the equation doesn’t cross theaxis.

Sample 3: Write the slope-intercept form of the line passing through the points (5, -5) and

(-5, -1).

Solution: First we find the slope:

Te Slope-intercept form is: