Presentation on theme: "Finding the Solutions, x-intercepts, Roots, or Zeros of A Quadratic"— Presentation transcript:
1 Finding the Solutions, x-intercepts, Roots, or Zeros of A Quadratic
2 x–Intercepts, Solutions, Roots, and Zeros in Quadratics x-intercept(s): Where the graph of y = ax2 + bx + c crosses the x-axis. The value(s) for x that makes a quadratic equal 0.Solution(s) OR Roots: The value(s) of x that satisfies 0 = ax2 + bx + c.Zeros: The value(s) of x that make ax2 + bx + c equal 0.
3 If a . b = 0, then a and or b is equal to 0 Zero Product PropertyIf a . b = 0, then a and or b is equal to 0Ex: Solve the following equation below.0 = ( x + 14 )( 6x + 1 )Would you rather solve the equation above or this: 0 = 6x2 + 85x + 14 ?
4 Use the Zero-Product Property ExampleSolve:Factor to rewrite as a productProductc(2x2)(-12)420x25Solve for 0 first!30x14x35ax2c12x22x30x xGCF___ax2bx6x744xUse the Zero-Product PropertySum
5 But this parabola has two zeros. ExampleUse the Zero Product Property to find the roots of:ProductBut this parabola has two zeros.(x2)(-7)-7x2c-7ax2cIMPOSSIBLEx2bx___ax2-3xSumJust because a quadratic is not factorable, does not mean it does not have roots. Thus, there is a need for a new algebraic method to find these roots.
6 Quadratic FormulaFor ANY 0 = ax2 + bx +c (standard form) the value(s) of x is given by:MUST equal 0Plus or MinusOpposite of b“All Over”This formula will provide the solutions (or lack thereof) to ANY Quadratic.
7 Example a = b = c = 1 -3 -4 Solve: Find the values of “a,” “b,” “c” Solve for 0 first!a = b = c =1-3-4Simplify the expression in the square root firstThe square root can be simplified.Substitute into the Quadratic FormulaOrSince the answers will be rational, it is best to list both.