4.8: Quadratic Formula HW: worksheet

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Presentation transcript:

4.8: Quadratic Formula HW: worksheet Academy Algebra II 4.8: Quadratic Formula HW: worksheet

Quadratic Formula The quadratic formula is used to solve a quadratic equation. Quadratic Formula: If ax2 + bx + c = 0, then

Discriminant The discriminant = b2 – 4ac The value of the discriminant tells you how many solutions the quadratic equation has. 0  1 real solution. positive number  2 real solutions. negative number  2 imaginary solutions.

Find the discriminant and determine the number of solutions. 1.) x2 – 8x + 16 = 0 2.) 5x2 + 20x = -21

Use the Quadratic Formula to find the solutions to the equation. 3.) x2 – 4x – 5 = 0

Use the Quadratic Formula to find the solutions to the equation. 4.) 3 – 8v – 5v2 = 2v

Use the Quadratic Formula to find the solutions to the equation. 5.) 4x2 + 3 = x2 – 7x

How to Solve Quadratics 1.) ax2 + bx + c = 0 Ex: 4x2 + 10x – 11 = 0 2.) ax2 + c = 0 Ex: x2 + 10 = 0 3.) a(x + b)2 + c = 0 Ex: 3(x – 1)2 – 8 = 0

Solve the equation. 1.) 7x – 3x2 = 85 + 2x2 + 2x 2.) 3x2 + x – 4 = 5x +

Solve the equation. 3.) 25 – 16x2 = 12x(x + 5) 4.) 19.25 = -8.5(2x – 1.75)2