Find the roots 1 x 2 64 0 2 8x 2 64x 0 3 x 2 16x 64 0 1 Ensure the quadratic equation is set to zero 2 Factor the quadratic equation GCF perfect square binomial DOTS trinomial ID: 619993
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Slide1
Aim
: How do we use quadratic equations to solve proportions?
Find the roots:
1) x
2
– 64 = 0
2) 8x
2
– 64x = 0
3) x
2
– 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
Slide2
1) x
2
– 64 = 0
2) 8x
2
– 64x = 0
3) x
2
– 16x + 64 = 0Slide3
Try these…
1)
2)
3)Slide4
You can do this!Slide5
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!Slide6
Practice Time!
1)
2)
3)
4)
5)Slide7
1)
2)Slide8
3)
4)
5)Slide9
How about this one?!
Which value of x is a solution of
-2
-3
-10-15Slide10
One More…
What is the solution set of:
Slide11
Aim: How
do we use quadratic
equations to solve
other problems?Do Now: Slide12
Procedure for Word Problems
1) Underline important words.
2) Translate into an equation.
3) Solve equation.4) Answer the question. Slide13
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?Slide14Slide15
Let’s challenge ourselves some more!
2.
Find three consecutive positive even
integers such that the product of the secondand third integers is twenty more than ten times the first integer. Slide16
**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?Slide17
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. Slide18
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? Slide19
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 + 16y = x2 – 9