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Quadratic Equations

Quadratic Equations. MTED 301 May 7, 2008 Diane Yum. Quadratic Equation. An equation that could be written as ax 2 +bx+c=0. Quadratic Equation. An equation that could be written as ax 2 +bx+c=0 Standard form of a quadratic equation ax 2 +bx+c=0. Quadratic Equation.

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Quadratic Equations

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  1. Quadratic Equations MTED 301 May 7, 2008 Diane Yum

  2. Quadratic Equation • An equation that could be written as ax2+bx+c=0

  3. Quadratic Equation • An equation that could be written as ax2+bx+c=0 Standard form of a quadratic equation ax2+bx+c=0

  4. Quadratic Equation • An equation that could be written as ax2+bx+c=0 Standard form of a quadratic equation ax2+bx+c=0 - The quadratic is on the left and 0 is on the right. - Moreover, it is standard for the leading coefficient A to be positive.

  5. 3 different ways to solve a quadratic equation

  6. 3 different ways to solve a quadratic equation • Solve by Factoring

  7. 3 different ways to solve a quadratic equation • Solve by Factoring • Solve by Completing the Square

  8. 3 different ways to solve a quadratic equation • Solve by Factoring • Solve by Completing the Square • Solve by Using “Quadratic Formula”

  9. Solving by Factoring • To solve a quadratic equation, • Put all terms on one side of the equal sign, leaving zero on the other side (Standard Form) • Factor • Set each factor equal to zero • Solve each of these equations • Check by inserting your answer in the original equation

  10. Example of factoring Ex) Solve for y: y2 = -6y – 5 First, change the equation into the standard form: y2 + 6y + 5 = 0 Factoring, (y+5) (y+1) = 0 Y+5 = 0 or y+1 = 0 Y = -5 or y = -1

  11. Check your answer (-5)2 = -6(-5) – 5 or (-1)2 = -6(-1) -5 25 = 30 – 5 1 = 6 - 5 25 = 25 1 = 1 You got it right 

  12. Solving by Completing the Square • Completing the Square: Finding something to add to a quadratic to make it a perfect square • Expression: (x+k)2 Applying our formula for squaring a binomial, we get (x+k)2 = x2 + 2xk + k2

  13. So if you have an expression of the form x2+bx and you want to find something to add to it to make it a perfect square, then you need to • Divide b by 2 to get k  • Square k to get k2 Ex) y2 – 9y

  14. Example of Completing the Square Ex) Solve x2 + 6x – 7 = 0 by completing the square • x2 + 6x – 7 = 0 • x2 + 6x = 7 • (6/2)2 = 9 • x2 + 6x + 9 = 7 + 9 • (x + 3 )2 = 16 • x + 3 = +4, -4 • x = -3 + 4 and -3 – 4 • x = +1 and -7

  15. Check your answer x2 + 6 x – 7 = 0 (1)2 + 6(1) – 7 = 0 and 1 + 6 – 7 = 0 You got it right again  x2 + 6x – 7 = 0 (-7)2 + 6(-7) – 7 = 0 49 – 42 - 7 = 0

  16. Solving by Quadratic Formula Quadratic Formula : Easy Steps to solve by quadratic formula • Find a, b, and c in the standard form • Substitute numbers of a, b, and c in the quadratic formula • Find the value of x

  17. Example of Quadratic Formula Ex) Solve the equation of 2x2 + 5x = 10 by using a quadratic formula ① Rewrite the equation into a standard form 2x2 + 5x – 10 = 0 ② Identify the values of a, b, and c a = 2, b = 5, c = -10 ③Substitute these values into the Quadratic Formula

  18. Substitution You can substitute the x values into the original equation to check the answer!

  19. Homework Due : Next Class Meeting

  20. Solve each equation by factoring, completing the square, or the quadratic formula. • Solve (x+1)(x-3) = 0 • Solve x2 + x – 4 = 0 • Solve x2 – 3x – 4 = 0 • Solve 6x2 + 11x – 35 = 0 • Solve x2 – 48 = 0

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