 ## Presentation on theme: "10-3: Solving Quadratic Equations"— Presentation transcript:

Essential Questions: How many solutions does a quadratic equation have? How can you determine the number of solutions from the graph?

The equation x2 + 3x – 4 = 0 is called a quadratic equation. It’s related to the quadratic function y = x2 + 3x – 4 The solutions of a quadratic equation and the x-intercepts of the quadratic function are the same A quadratic equation can have one, two, or no real-number solutions. The solutions of a quadratic equation and the x-intercepts are often called the roots of the equation or zeros of the function.

Example 1a: Solving by Graphing (Two solutions) Solve each equation by graphing the related function x2 – 4 = 0 Graph y = x2 – 4 Solutions are where the graph crosses the x-axis. There are two solutions here x = 2 or x = -2, which can be written as x = ±2

Example 1b: Solving by Graphing (1 solution) Solve each equation by graphing the related function x2 = 0 Graph y = x2 Solutions are where the graph crosses the x-axis. There is one solution here x = 0

Example 1c: Solving by Graphing (0 solutions) Solve each equation by graphing the related function x2 + 4 = 0 Graph y = x2 + 4 Solutions are where the graph crosses the x-axis. Since the graph never crosses the x-axis, there is no solution

Solving Quadratic Equations Using Square Roots We can solve equations in the form x2 = c by finding the square roots of each side. Solve 2x2 – 98 = 0 2x2 – 98 = Add 98 to each side 2x2 = 98 ÷ ÷2 Divide each side by 2 x2 = 49 x = ± Take the square root of 49 x = ±7 Remember the ±