1. Aim: How do we use quadratic equations to solve proportions
Aim: How do we use quadratic equations to solve proportions? Find the roots: 1) x2 – 64 = 0 2) 8x2 – 64x = 0 3) x2 – 16x + 64 = 0 1) Ensure the quadratic equation is set to zero. 2) Factor the quadratic equation (GCF, perfect square binomial [DOTS], trinomial) 3) T-chart 4) Solve for x
Do now with perfect squares binomials (DOTS), regular binomial and trinomial
identify

2. 1) x2 – 64 = 0 2) 8x2 – 64x = 0 3) x2 – 16x + 64 = 0

3. Try these… 1) 2) 3)

4. You can do this!

5. Steps for solving proportions involving quadratics
Cross Multiply
Put the equation in standard form
(0 = ax2 + bx + c)
3. Factor to solve
Yes, you need to copy these!

6. Practice Time! 1) 2) 3) 4) 5)

7. 2) 1)

8. 3) 4) 5)

9. How about this one?! Which value of x is a solution of -2 -3 -10 -15
X = -15, x = 2

10. One More…
What is the solution set of:
X = -6, x = 1

11. Aim: How do we use quadratic equations to solve other problems?
Do Now:

12. Procedure for Word Problems
1) Underline important words.
2) Translate into an equation.
3) Solve equation.
4) Answer the question.

13. Let’s challenge ourselves!
When 36 is subtracted from the square of a number, the result is five times the number. What is the positive solution?
1. x = 9 2. (6,8,10)

15. Let’s challenge ourselves some more!
2. Find three consecutive positive even integers such that the product of the second and third integers is twenty more than ten times the first integer.
1. x = 9 2. (6,8,10)

16. **Super-Challenge!** 3. Max has 2 sisters. One of the sisters is
two years older than Max. The other sister is
3 years younger than Max. The product of
Max’s sister’s ages is 24. How old is Max?

17. Can you handle one more??
4. The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle.

18. What Have You Learned? How do you solve a proportion?
How do you put an equation into standard form?
What are the steps for solving a proportion involving a quadratic equation?

19. Throw Backs
Find the vertex and the axis of symmetry for the following quadratic equation:
Find the roots by factoring:
y = x2 – x – 6
y = x2 – 8x + 16
y = x2 – 9