Exam 10: Section 2: Quadratic Equations and Inequalities

Find the imaginary solutions: x² - 6x + 90 = 0

Solve the inequality. Graph the solution set. x² - 8x + 12 < 0

Solve using the quadratic formula: 3x² + 5x - 1 = 0

Graph the parabola. y = -x² + 4

Solve the given inequality and express the solution in interval notation. x² - 4x  0

Find all real and imaginary solutions to the equation. t⁴ - 6561 = 0

Write a quadratic equation that has the solutions 8 and 1.

Terrence paddles his canoe upstream a distance of 6 miles. He completes the return trip in 30 minutes less that the upstream journey. If the current flows at 4 miles per hour, what is Terrence's speed in still water?

If an object is given an initial velocity of v₀ feet per second from a height of s₀ feet, then its height S after t seconds is given by the formula . A rock is thrown into the air at 42 feet per second from a height of 21 feet. How long does it take to reach the earth?

Complete the ordered pair so that it satisfies the given equation. y = x² + 4x + 2, (4, )

Find all real and imaginary solutions to the equation. x^-2 - 3x^-1 + 5 = 0

Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 7x² + 7x + 9

Find all intercepts for the graph of the parabola. f(x) = 49 - x²

Find all real solutions of the given equation. x^2/3 - 3x^1/3 - 10 = 0

Find the vertex for the graph of the parabola. f(x) = x² - 5

Solve by factoring: x² - 5x - 50 = 0

The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x² - 6x - 7. For what values of x is her profit positive?

A battery manufacturing plant spends C dollars per hour to produce "D"-size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x) = 0.02x² - 3x + 217.5. What number of batteries per hour minimizes the cost?

Solve:

Solve: (q - 6)² = 36