5.5 Quadratic Formula

Warm-up (IN)

Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find the axis of symmetry of the

parabola

Evaluate the expression for the given values of a, b, and c.

1. a=1, b=3, c=-12. a=2, b=-2, c=03. a=-1, b=0, c=54. a=-2, b=2, c=-3

2 4b ac

20

13

4

20

Notes

Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find the axis of symmetry of the parabola

2if 0, thenax bx c

2 4

2

b b acx

a

**Quadratic Formula -

EX 1 – Solve: 2a. 3 8 35x x

23 8 35 0x x a

b

c

x 8 28 4 3 35

2 3x 8 64 420

6

x 8 4846

8 22

6

x 146

73

x 306

5

Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find the axis of symmetry of the parabola

2b. 12 5 2 13x x

22 12 18 0x x a

b

c

x 12 212 4 2 18

2 2x 12 144 144

4

x 12 0

43

Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find the axis of symmetry of the parabola

**equation for axis of symmetry – 2

bx

a

it’s also the x-coordinate of the vertex!

EX 2 – let , write an equation for the axis of symmetry and find the coordinates of the vertex.

22 3 2f x x x

22 2 3f x x x 21 1

2 2 32 2

y

12 1 3

4y

1

22

y 5

2y

x 2

2 21

21 5

,2 2

V x 1

2

HW – p. 311 #12-45 mult. of 3, 49-51

Out – How is the axis of symmetry related to the vertex of a parabola?

Summary – Today, I learned…

POW!!