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**Thompsonnn****Member**- Registered: 2017-08-01
- Posts: 19

10. Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

11. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

12. Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.)

18. A tennis ball is launched straight upward with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:

4.9t2 + 24.5t + 117.6 = 0

-4.9t2 - 24.5t + 117.6 = 0

-4.9t2 + 24.5t - 117.6 = 0

4.9t2 + 24.5t - 117.6 = 0

-4.9t2 + 24.5t + 117.6 = 0

19. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)

t = 8 seconds

t = 4 seconds

t = 3 seconds

t = -3 seconds

The ball will never reach the ground.

20. Using the same equation, determine when the ball is at a height of 49 meters.

*Last edited by Thompsonnn (2017-08-02 00:25:56)*

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Hi Thompsonnn,

Welcome to the forum. Let's start with questions 10-12. Have you made any attempts at these? What is the relationship between a quadratic's roots and its factors?

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
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For a hint, no. 10 is like this:

(x - 3) (x + 7) = 0

Continue and simplify the term. Once you get a grasp, you can just follow the pattern for no. 11 and 12.

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**ImpossibleTriangle****Member**- Registered: 2017-07-31
- Posts: 6

Hi;

The only way to learn mathematics is to do mathematics. ~Paul Halmos

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**Thompsonnn****Member**- Registered: 2017-08-01
- Posts: 19

x-3=0, x+7=0

(x-3)(x+7)=0

(x-3)(x+7)=x2+4x-21

This is one of my attempts for number 10.

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That is correct. Are you able to do the others?

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**Thompsonnn****Member**- Registered: 2017-08-01
- Posts: 19

x-12=0, x-2=0

(x-12)(x-2)=0

x2-2x-14+24 =0

This is for number 11.

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Well done! How about the next one?

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**Thompsonnn****Member**- Registered: 2017-08-01
- Posts: 19

12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x =4.

(x+.5)(x-4)=0

2x2-7x-4 =0

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**Thompsonnn****Member**- Registered: 2017-08-01
- Posts: 19

The one i have trouble on is 18-20

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Your answer for Q12 is correct.

For Q18, you'll need to use your SUVAT equations. You know your initial velocity (that's ). We want to find . We take gravity, , to be . You want to know the time when the particle hits the ground, which is below where the particle has been launched from (so, you'll want ). With these in mind, which equation should you use?

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**Thompsonnn****Member**- Registered: 2017-08-01
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-4.9t2 + 24.5t + 117.6 = 0 this is what i got for 18.

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That looks correct. How about the last two?

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**Thompsonnn****Member**- Registered: 2017-08-01
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im not sure how to do the last 2.

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Do you know how to solve a quadratic equation?

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**Thompsonnn****Member**- Registered: 2017-08-01
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im not to sure how

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Our quadratic equation is Let's divide both sides by so we have nice, whole numbers to deal with instead. We'll get:

Can you solve this by factoring?

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**Thompsonnn****Member**- Registered: 2017-08-01
- Posts: 19

5t^2-24=0

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Here's a quick way to factor We want to find two numbers such that:-They add to make , and

-They multiply to make .

-They multiply to make .

For instance, -6 and 1 add to make -5, but their product is -6, so that doesn't work.

However, -8 and 3 add to make -5, and their product is -24, so that's the correct combination. Thus, we can factor like this:

Are you able to solve the question from here?

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**Thompsonnn****Member**- Registered: 2017-08-01
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t^2-8t+3t-24=0?

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That is what happens when you expand the brackets, but what are the solutions to the quadratic equation ? (Think back to questions 10-12...)

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**Thompsonnn****Member**- Registered: 2017-08-01
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t^2-11t-24

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For which values of is equal to ?

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**Thompsonnn****Member**- Registered: 2017-08-01
- Posts: 19

should i distribute the t?

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Thompsonnn wrote:

10. Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

Remember that here we wanted a quadratic equation with factors (x - 3) and (x + 7), because those equal zero when x = 3 and x = -7, respectively.

So a quadratic equation that has solutions x = 3 and x = -7 is (x - 3)(x + 7) = 0.

This time, you're given the quadratic equation (t - 8)(t + 3) = 0.

This has factors (t - 8) and (t + 3).

Can you see which values of t will make those equal zero?

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