Place your final answers in simple radical form. In Exercises 37-52, find all real solutions, if any, of the given equation. Check your answer by factoring your result. In Exercises 25-36, for each expression, complete the square to form a perfect square trinomial. In Exercises 19-24, factor each of the following trinomials. In Exercises 13-18, square each of the following binomials. In Exercises 9-12, find all real solutions of the given equation. ![]() In Exercises 1-8, find all real solutions of the given equation. If the base of the ladder is \(6\) feet from the garage wall, how high up the garage wall does the ladder reach? Use your calculator to round your answer to the nearest tenth of a foot. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as completing the square. In elementary algebra, the quadratic formula is a formula that provides the two solutions, or roots, to a quadratic equation. ![]() AnswerĤ0) A ladder \(19\) feet long leans against the garage wall. The quadratic function y 1 2 x2 5 2 x + 2, with roots x 1 and x 4. If the base of the ladder is \(5\) feet from the garage wall, how high up the garage wall does the ladder reach? Use your calculator to round your answer to the nearest tenth of a foot. Find the lengths of all three sides of the right triangle.ģ9) A ladder \(19\) feet long leans against the garage wall. The hypotenuse is \(3\) feet longer than twice the length of the shorter leg. Answerģ8) The longest leg of a right triangle is \(2\) feet longer than twice the length of its shorter leg. Find the lengths of all three sides of the right triangle. The hypotenuse is \(4\) feet longer than three times the length of the shorter leg. What is the area of the shaded region?ģ7) The longest leg of a right triangle is \(10\) feet longer than twice the length of its shorter leg. What is the area of the shaded region? Answerģ6) In the figure below, a right triangle is inscribed in a semicircle. Your final answer must be in simple radical form.ģ5) In the figure below, a right triangle is inscribed in a semicircle. In Exercises 27-34, find the length of the missing side of the right triangle. In Exercises 7-26, convert each of the given expressions to simple radical form. Check the result with your graphing calculator. In Exercises 1-6, simplify the given expression, writing your answer using a single square root symbol. Second, solve the equation algebraically, then use your calculator to find approximations of your answers and compare this second set with the first set of answers. Follow the Calculator Submission Guidelines, as demonstrated in Example 8.1.9 in reporting the solution on your homework paper. In Exercises 39-42, for each of the given equations, first use the 5:intersect utility on the CALC menu of the graphing calculator to determine the solutions. In Exercises 31-38, simplify each of the given expressions. In Exercises 21-30, simplify each of the given expressions. Any other quadratic equation is best solved by using the Quadratic Formula.=324\). If the equation fits the form \(ax^2=k\) or \(a(x−h)^2=k\), it can easily be solved by using the Square Root Property. If the quadratic factors easily this method is very quick. To identify the most appropriate method to solve a quadratic equation:.if \(b^2−4acif \(b^2−4ac=0\), the equation has 1 solution.if \(b^2−4ac>0\), the equation has 2 solutions.import complex math module import cmath a 1 b 5 c 6 To take coefficient input from the users a float (input. we already know that the solutions are x 4 and x 1. This quadratic happens to factor: x2 + 3x 4 (x + 4) (x 1) 0. Using the Discriminant, \(b^2−4ac\), to Determine the Number of Solutions of a Quadratic Equationįor a quadratic equation of the form \(ax^2+bx+c=0\), \(a \ge 0\) , Below is the Program to Solve Quadratic Equation.Then substitute in the values of a, b, c. Write the quadratic formula in standard form.To solve a quadratic equation using the Quadratic Formula. ![]() Solve a Quadratic Equation Using the Quadratic Formula.Quadratic Formula The solutions to a quadratic equation of the form \(ax^2+bx+c=0\), \(a \ge 0\) are given by the formula:.The equation is in standard form, identify a, b, c.īecause the discriminant is negative, there are no real solutions to the equation.īecause the discriminant is positive, there are two solutions to the equation.īecause the discriminant is 0, there is one solution to the equation. This last equation is the Quadratic Formula.ĭetermine the number of solutions to each quadratic equation:
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