Objective: The learner will..,

1 / 20

# Objective: The learner will.., - PowerPoint PPT Presentation

10.4 Solving Quadratic Equations . Objective: The learner will..,. NCSCOS. Solve quadratic equations by factoring, completing the square finding the vertex, AOS, and zeros. Find the two ordered pairs for the intersection of the parabola and the linear equation. 1.01, 4.02.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Objective: The learner will..,' - bertha

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Objective: The learner will..,

NCSCOS

• Solve quadratic equations by factoring, completing the square finding the vertex, AOS, and zeros.
• Find the two ordered pairs for the intersection of the parabola and the linear equation.
• 1.01, 4.02

10.1 Graphing Parabolas

Factor, find the AOS, and the Vertex:

y = x2– 6x + 8

x2– 6x + 8 = 0

x2– 6x + 8 = 0

(x– 2)(x– 4) = 0

(3)2– 6(3) + 8 = 0

x = 2 x = 4

(x– 2) = 0 (x– 4) = 0

-1

9 – 18 + 8 =

Find the AOS:

vertex: (3, )

-1

2 + 4

Find the vertex form:

=3

x =

2

y = (x – 3)2–1

AOS:3

10.1 Graphing Parabolas

Factor, find the AOS, and the Vertex:

y = x2 + 2x – 24

x2 + 2x –24 = 0

x2 + 2x – 24 = 0

(x + 6)(x– 4) = 0

(–1)2 + 2(–1) – 24 = 0

x = 4 x = –6

(x– 4) = 0 (x + 6) = 0

–25

1 – 2 – 24 =

Find the AOS:

–25

vertex: (-1, )

4 – 6

Find the vertex form:

=–1

x =

2

y = (x+1)2–25

AOS:–1

10.1 Graphing Parabolas

Factor, find the AOS, and the Vertex:

y = x2– 6x + 5

x2– 6x + 5 = 0

x2– 6x + 5 = 0

(3)2– 6(3) + 5 = 0

(x– 1)(x– 5) = 0

-4

9 – 18 + 5 =

x = 1 x = 5

(x– 1) = 0 (x– 5) = 0

vertex: (3, )

-4

Find the AOS:

Find the vertex form:

1 + 5

=3

x =

2

y = (x – 3)2–4

AOS:3

Complete the Square to find the vertex, AOS, and zeros:

y = x2 – 4x + 1

y = x2 – 6x + 7

(x2 – 4x+ 4) + 1 – 4 = 0

(x2 – 6x+ 9) + 7 – 9 = 0

(x – 2)2 – 3 = 0

(x – 3)2 – 2 = 0

Vrtx:

(2, –3)

AOS:

Vrtx:

2

(3, –2)

3

AOS:

(x – 2)2 – 3 = 0

(x – 3)2 – 2 = 0

(x – 2)2 = 3

(x – 3)2 = 2

x – 2 = ± 1.73

x – 3 = ± 1.41

x = 3.7 & .27

x = 4.41 & 1.59

Complete the Square to find the vertex, AOS, and zeros:

y = x2 – 8x + 3

y = x2 – 10x + 23

(x2 – 8x + 16) + 3 – 16 = 0

(x2 – 10x + 25) + 23 – 25 = 0

(x – 4)2 – 13 = 0

(x – 5)2 – 2 = 0

Vrtx:

(4, -13)

AOS:

4

(5, -2)

Vrtx:

5

AOS:

(x – 4)2 – 13 = 0

(x – 5)2 – 2 = 0

(x – 4)2 = 13

(x – 5)2 = 2

x – 4 = ± 3.61

(x – 5) = ±1.41

x = 7.6 & .39

x = 6.4 & 3.6

Complete the Square to find the vertex, AOS, and zeros:

x2 – 8x + 3 = 0

x2 + 6x + 4 = 0

(x2 – 8x + 16) + 3 – 16 = 0

(x2 + 6x + 9) + 4 – 9 = 0

(x – 4)2 – 13 = 0

(x + 3)2 – 5 = 0

4

(4, –13)

AOS:

Vrtx:

-3

(-3, -5)

Vrtx:

AOS:

(x – 4)2 – 13 = 0

(x + 3)2 – 5 = 0

(x – 4)2 = 13

(x + 3)2 = 5

x – 4 =  3.61

x + 3 =  2.24

x = .39 & 7.6

x = -0.76 & -5.24

Complete the Square to find the vertex, AOS, and zeros:

x2 + 2x – 7 = 0

x2 – 4x – 1 = 0

(x2 + 2x + 1) – 7 – 1 = 0

(x2 – 4x + 4) – 1 – 4 = 0

(x + 1)2 – 8 = 0

(x – 2)2 – 5 = 0

-1

Vrtx:

(2, -5)

(-1, -8)

2

Vrtx:

AOS =

AOS:

(x – 2)2 – 5 = 0

(x + 1)2 – 8 = 0

(x – 2)2 = 5

(x + 1)2 = 8

x – 2 =  2.24

x + 1 =  2.83

x = -0.24 & 4.24

x = -3.83 & 1.83

Find the two ordered pairs for the intersection of the parabola and the linear equation.

y = x2 + 3x – 15 and y = -5

x2 + 3x – 15 = -5

x2 + 3x – 10 = 0

y = -5

-5

(-5, )

(x + 5)(x – 2) = 0

(x + 5) = 0

x = -5

y = -5

(x – 2) = 0

x = 2

(2, )

-5

Find the vertex, AOS, and x-intercepts:

y = x2 + 3x – 15 and y = -5

(x2 + 3x + 2.25) – 15 – 2.25

(x + 1.5)2 – 17.25

Vrtx: (–1.5, –17.25)

AOS: –1.5

x2 + 3x – 15 = 0

(x + 5)(x – 3) = 0

(2,-5)

(-5,-5)

x = –5 & 3

(2, -5)

(-5, -5)

Find the two ordered pairs for the intersection of the parabola and the linear equation.

y = x2 – 10x + 21 and y = x – 3

y = x – 3

x2 – 10x + 21 = x – 3

y = 8 – 3

x2 – 11x + 24 = 0

y = 5

(x – 8)(x – 3) = 0

5

(8, )

(x – 8) = 0

x = 8

y = x – 3

x = 3

(x – 3) = 0

y = 3 – 3

y = 0

0

(3, )

Find vertex, AOS, and x-intercepts then graph the parabola and linear equation:

y = x2 – 10x + 21 and y = x – 3

(x2 – 10x + 25) + 21 – 25

(x – 5)2 + 21 – 25

(x – 5)2 – 4 = 0

Vrtx: (5, –4)

(8,5)

AOS: 5

(x – 5)2 = 4

(3,0)

x – 5 =  2

x = 7 & 3

(3, 0) (8, 5)

Find the two ordered pairs for the intersection of the parabola and the linear equation.

y = x2 – 4x + 1 and y = -2x + 4

y = -2x + 4

x2 – 4x + 1 = -2x + 4

y = -2(-1) + 4

x2 – 4x + 2x + 1 – 4 = 0

y = 6

x2 – 2x – 3 = 0

(-1, )

6

(x + 1)(x – 3) = 0

y = -2x + 4

(x + 1) = 0

x = -1

y = -2(3) + 4

x = 3

(x – 3) = 0

y = -2

-2

(3, )

Find vertex, AOS, and x-intercepts then graph the parabola and linear equation:

y = x2 – 4x + 1 y = -2x + 4

(x2 – 4x + 4) + 1 – 4

(x – 2)2 + 1 – 4

(-1,6)

(x – 2)2 – 3 = 0

V (2, –3)

(x – 2)2 = 3

(3,-2)

x – 2 =  1.73

x = 3.73 & .27

(-1, 6) (3, -2)

Find the two ordered pairs for the intersection of the parabola and the linear equation.

y = x2 – 4x + 11 and y = x + 5

y = x + 5

x2 – 4x + 11 = x + 5

y = (2) + 5

x2 – 5x + 6 = 0

y = 7

(2, )

7

(x – 2)(x – 3) = 0

y = x + 5

(x – 2) = 0

x = 2

y = (3) + 5

(x – 3) = 0

x = 3

y = 8

(3, )

8

Find vertex, AOS, and x-intercepts then graph the parabola and linear equation:

y = x2 – 4x + 11 and y = x + 5

(x2 – 4x + 4) + 11 – 4

(x – 2)2 + 11 – 4

(x – 2)2 + 7 = 0

Vrtx: (2, 7)

(3,8)

AOS: 2

(2,7)

(x – 2)2 = –7

Can’t take the sq root; no x-intercepts

(2, 7) (3, 8)

Find the two ordered pairs for the intersection of the parabola and the linear equation.

y = x2 – 7x + 10 and y = x – 2

y = x – 2

x2 – 7x + 10 = x – 2

y = 6 – 2

x2 – 8x + 12 = 0

y = 4

(x – 6)(x – 2) = 0

4

(6, )

(x – 6) = 0

x = 6

y = x – 2

x = 2

(x – 2) = 0

y = 2 – 2

y = 0

0

(2, )

Find vertex, AOS, and x-intercepts then graph the parabola and linear equation:

y = x2 – 7x + 10 and y = x – 2

(x2 – 7x + 12.25) + 10 – 12.25

(x – 3.5)2 + 10 – 12.25

(x – 3.5)2 – 2.25 = 0

Vrtx: (3.5, –2.25)

AOS: 3.5

(x – 3.5)2 = 2.25

x – 3.5 =  1.5

x = 5 & 2

(2, 0) (6, 4)

(2,0)

(6,4)

Find the two ordered pairs for the intersection of the parabola and the linear equation.

y = x2 – x – 9 and y = –2x – 3

(–3, 3) and (2, –7)

y = x2 – 4x + 3 and y = x + 3

(0, 3) and (5, 8)

y = x2 – 8x + 5 and y = 2x – 4

(1, –2) and (9, 14)

Find the two ordered pairs for the intersection of the parabola and the linear equation.

y = x2 + 6x + 8 and y = 2x + 8

(–4, 0) and (0, 8)

y = x2 + 4x – 5 and y = −2x – 5

(−6, 7) and (0, −5)

y = x2 – 6x + 9 and y = x – 3

(3, 0) and (4, 1)