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Review – Quadratic Equations

Review – Quadratic Equations. • All quadratic equations do not look the same, but they all can be written in the general form. y = a · x 2 + b · x + c. where a , b , and c are numbers and a does not equal 0. • Here are some examples of quadratic equations.

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Review – Quadratic Equations

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  1. Review – Quadratic Equations • All quadratic equations do not look the same, but they all can be written in the general form. y = a·x2 + b·x + c where a, b, and c are numbers and adoes not equal 0. • Here are some examples of quadratic equations 2x2 + 5x + 1 = 0 x2 - 10x + 11 = 0 x2 + 30x = 0 -7x2 - 28 = 0

  2. Review – Quadratic Equations • A good first step to take when solving a quadratic equation is to put the equation in the general form. 36 - 5x = x2 x2 + 5x - 36 = 0 • Once you have it in general form, there are several ways that you can find the value(s) of x. 1. If the “b” term is missing, then solve the equation as normal. 8x2 - 48 = 0

  3. Review – Quadratic Equations 2. If the “c” term is missing, then factor and solve. Ex1) x2 + 9x = 0 Ex2) 3x2 - 6x = 0 3. If all of the terms are there, then you have two options. a. Find the factored form and solve. x2 + 5x - 36 = 0 b. Use the quadratic formula

  4. Fireworks – Quadratic Formula • The quadratic formula can be used to find the solutions, or x-intercepts, of any quadratic function in the form: y = a·x2 + b·x + c where y = 0. • The quadratic formula is… all you have to do is substitute for the missing values and evaluate.

  5. a = 2 b = 5 c = 1 Fireworks – Quadratic Formula • An example: 2x2 + 5x + 1 = 0

  6. a = –0.5 b = –1 c = 9 Fireworks – Quadratic Formula • Another… : – 0.5x2–x + 9 = 0

  7. Fireworks – Quadratic Formula • The quadratic formula can be used to find the solutions, or x-intercepts, of any quadratic function in the form: y = a·x2 + b·x + c where y = 0. • The quadratic formula is… all you have to do is substitute for the missing values and evaluate.

  8. a = 2 b = 5 c = 1 Fireworks – Quadratic Formula • An example: 2x2 + 5x + 1 = 0

  9. a = –0.5 b = –1 c = 9 Fireworks – Quadratic Formula • Another… : – 0.5x2–x + 9 = 0

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