Presentation on theme: "A quadratic equation is a equation that can be written in the form."— Presentation transcript:
A quadratic equation is a equation that can be written in the form
Quadratic equation can be solved by a variety of methods Graphing Squared Root property Factoring Completing the square Quadratic formula
A quadratic equation can have two, one or no real number solutions The solutions of a quadratic equation are the x- intercepts of the related function The solutions of a quadratic equation are often called Roots of the equation or Zeros of the function
Steps in Solving Quadratic Equations 1)If the equation is in the form (ax+b) 2 = c, use the square root property to solve. 2)If not solved in step 1, write the equation in standard form. 3)Try to solve by factoring. 4)If you haven’t solved it yet, use the quadratic formula.
Graph the parabola by: 2-2 Finding the equation of the axis of symmetry Making a table using the x-values around the axis of symmetry Graphing each point on a coordinate plane The roots of the equation or solution are the x-intercept or zeros of the related quadratic function xy 20 -20
What are the solution of each equation? Use a graph of the related function There are two solutions 1 and -1 There is one solutions 0 There is no real number solution
You can solve equations of the form Square Root Property If b is a real number and a 2 = b, then by finding the square root of each side. For example
Solve: A) (y – 3) 2 = 4 Example
This method will work to solve ALL quadratic equations For many equations it takes longer than some of the other methods.
A quadratic equation written in standard form, ax 2 + bx + c = 0, has the solutions. When getting your solution, if the radicand in the quadratic formula is not a perfect square, you can use a calculator to approximate the solution
x 2 + 8x – 20 = 0 (multiply both sides by 8) a = 1, b = 8, c = 20 Solve x 2 + x – = 0 by the quadratic formula. Example
Solve x(x + 6) = 30 by the quadratic formula. So there is no real solution. Square root can’t be negative. Example (Simplify the polynomial and write it on standard form) x 2 + 6x + 30 = 0 a = 1, b = 6, c = 30
Solve 2x = x 2 - 8. write the equation on standard form x 2 – 2x – 8 = 0 Let a = 1, b = -2, c = -8 Example
Before you solve a quadratic equation you can determine how many real-number solutions it has by using discriminant. The expression under the radical sign in the formula (b 2 – 4ac) is called the discriminant. The discriminant will take on a value that is positive, 0, or negative. The value of the discriminant indicates two distinct real solutions, one real solution, or no real solutions, respectively.
Use the discriminant to determine the number and type of solutions for the following equation. 5 – 4x + 12x 2 = 0 a = 12, b = –4, and c = 5 b 2 – 4ac = (–4) 2 – 4(12)(5) = 16 – 240 = –224 Because the discriminant is negative, the equation has no-real number solution. Example