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Using the Zero-Product Property to Solve a Quadratic

Using the Zero-Product Property to Solve a Quadratic. x–Intercepts, Solutions, Roots, and Zeros in Quadratics. x-intercept(s): Where the graph of y=ax 2 +bx+c crosses the x-axis . The value(s) for x that makes a quadratic equal 0 .

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Using the Zero-Product Property to Solve a Quadratic

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  1. Using the Zero-Product Property to Solve 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. Zero Product Property If a . b = 0, then a and or b is equal to 0 Ex: Solve the following equation below. 0 = ( x + 14 )( 6x + 1 ) OR Would you rather solve the equation above or this:0 = x2 + 25x + 14 ?

  4. Solving a Quadratic: Factoring Solve: Product (2x2)(-12) -24x2 c Factor to rewrite as a product 4 -12 8x -3x ax2c 8x -3x 2x2 GCF x bx ___ ax2 5x 2x -3 Use the Zero-Product Property Sum

  5. Solving a Quadratic: Already Factored Solve: The equation is already factored AND it equals 0. Half the work is already done. Just use the Zero-Product Property

  6. Solving a Quadratic: Making Sure to Isolate 0 Solve: Factor to rewrite as a product Product c (2x2)(-12) 420x2 5 35 30x 14x Solve for 0 first! ax2c 12x2 30x 14x 2x GCF ___ bx ax2 6x 7 44x Use the Zero-Product Property Sum

  7. Solving a Quadratic: Make Sure to Isolate 0 Solve: Factor to rewrite as a product Product c (x2)(-4) -4x2 -4 -4 -4x x Solve for 0 first! Distribute ax2c x2 -4x 1x x GCF ___ bx ax2 x 1 -3x Use the Zero-Product Property Sum

  8. Do we Need Another Method? Use the Zero Product Property to find the roots of: Product But this parabola has two zeros. (x2)(-7) -7x2 c -7 ax2c IMPOSSIBLE x2 bx ___ ax2 -3x Sum Just 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.

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