(3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · find...

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What are the roots? (3x + 4)(2x + 7) = 0

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Page 1: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

What are the roots?

(3x + 4)(2x + 7) = 0

Page 2: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Solve for t.

20 48 16t t

Page 3: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Then name the vertex, axis of symmetry,

stretch and the direction of the opening.

1)3(4)( 2xxf

Page 4: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Solve by using factoring.

300 2 yy

Page 5: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Find the equation in standard form

with the roots of 5 and -3.

Page 6: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Find the value of the discriminant for each

quadratic equation. Then describe the nature

of the roots.

042 2x

Page 7: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Use quadratic formula to solve each

equation.

443 2 xx

Page 8: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

.167.57)(

formula by thegiven is thrown isit after seconds t ball theofheight The

second.per feet 57.7 of velocity initialan with upstraight thrown is ballA

2ttth

height? maximum its is What

Page 9: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

584 2 xx

Solve for x.

Page 10: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Write the inequality for the graph (leave in factored form)

Page 11: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

2

1)( 2attvtd i

The distance that an object travels can be calculated by the initial

speed vi, elapsed time t, and the rate of acceleration a are known.

If a motorcycle has an initial speed of 30 m/s and acceleration of 6 m/s2,

how much time will it take to travel 200 meter?

Page 12: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Solve the system.

Page 13: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

The product of two consecutive

negative even integers is 24. Find

the integers.

Page 14: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Factor.

23 11152 rrr

Page 15: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Use quadratic formula to solve each

equation.

652 2 xx

Page 16: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Find the equation in standard form

with the roots of 3 and -3 with a

vertex at (0,4.5)

Page 17: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Find the value of the discriminant for

each quadratic equation. Then describe

the nature of the roots.

1682 xx

Page 18: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

The length of a rectangle is three

more than twice the width.

Determine the dimensions that will

give the rectangle a total area of 27

m2.

Page 19: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Solve for x.

10133 2 xx

Page 20: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Find the value of the discriminant for each

quadratic equation. Then describe the nature

of the roots.

049142 xx

Page 21: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Write a quadratic equation that has

roots 6 and -9.

Page 22: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Write the inequality for the graph (leave in factored form)

Page 23: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

Solve the system.

Page 24: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

A sidewalk of uniform width is to be

built around a rectangular 8 m x 10 m

garden. If the area of the sidewalk is

to be one half the area of the garden,

how wide should the sidewalk be?

Page 25: (3x + 4)(2x + 7) = 0danielsroar.weebly.com/uploads/5/3/1/4/5314494/quadratics_review_… · Find the equation in standard form with the roots of 3 and -3 with a vertex at (0,4.5)

1. x = -4/3 or -7/2

2. t = 0 or 3

3. Vertex: -3, -1 aos: x = -3

stretch 4 open up

4. Y = -6 or 5

5. x2 – 2x – 15

6. Discriminant -32

2 imaginary

7. x = 2/3 or -2

8. 52.02 ft

9. x = -.5 or 2.5

10. y<(x+3)(x-5)

11. 4.57 sec

12. (-4,-1) (1,4)

13. -6 and -4

14. r = 0, 5/2 or 3

15. (4+- sqrt(73))/4

16. -0.5x^2+4.5

17. -52, 2

imaginary roots

18. 3x9 m

19. 10/3 or ½

20. 0, 1 real rational

21. x2+3x-54

22. Y>= (x+1)2

23. (-1,4) (2,7)

24. 1 m