08 - Factored Form to Standard Form PDF

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8 - Factored Form to Standard Form

MPM2D – Introduction to Quadratics

Date: ______________________________________________

Factored Form to Standard Form Recall:

New:

Factored Form:  = !"# − %&"# − '&

Standard Form:  = !# ( + *# + +

To convert the equation of a quadratic relation from factored form to standard form, we will expand using the distributive property and simplify the factored form.

Example 1 Rewrite  = "# + 2&"# + 1& in standard form.

Example 2 Rewrite  = "# − 2&"# + 1& in standard form.

Example 3 Rewrite the following in standard form:  = 3"# − 1&"# − 5&

 = "2# − 1&"3# + 4 &

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8 - Factored Form to Standard Form

MPM2D – Introduction to Quadratics

Example 4 Determine the equation of this parabola, in standard form.

Example 5 The point "−3, −4& lies on the parabola which has zeros at –1 and –5. Determine the equation of this parabola in standard form.

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8 - Factored Form to Standard Form

MPM2D – Introduction to Quadratics

Homework 1. Expand and simplify each expression. a. "/ − 2&"/ + 3&

b. "# + 5&"# + 2&

c. "! − 2&"! − 7 &

d. "2# + 3&"# − 4&

e. "% − 2 &"3% + 1&

f.

"2# + 1&"# − 5&

g. "3# − 2&"4# + 3&

h. −"2# + 5&"3# − 1&

i.

−2"5# − 2&"3# + 4 &

2. Determine the equation for each of the following parabolas in both factored form and standard form.

3. For each quadratic relationship, write the equation in standard form. Zeros

Point on the Graph

a.

–1 and 7

"3,5&

b.

–1 and 5

"−3,−4&

c.

3 and 7

"0,3&

d.

–2 and 6

"−1,−1&

e.

–2 and 8

"3,7&

4. A parabolic arch has a base of 192 m across and reaches 192 m high. Determine the equation of this arch in standard form. 5. What is the length of the missing side of this rectangle?

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8 - Factored Form to Standard Form

MPM2D – Introduction to Quadratics

Answers 1. a. / ( + / − 6

b. # ( + 7# + 10

c. !( − 9! + 14

d. 2# ( − 5# − 12

e. 3% ( − 5% − 2

f.

2# ( − 9# − 5

g. 12# ( + # − 6

h. −6# ( − 13# + 5

i.

−30# ( − 28# + 16

2. 4

4

a.  = "# + 3&"# − 2&

b.  = − "# + 4&"2# − 1&

c.  = "# − 3&"# − 7&

 = #( + # − 6

 = −# ( − 3.5# + 2

 =5 #( − # +

(

5

4

7

(4

(

5

3. 7

9:

97

a.  = − 48 # ( + 48 # + 48 4

5

d.  = ; # ( − ; # −

4.  = −

4 5<

4( ;

4

7

5

5

b.  = − # ( + # + ;

5(

e.  = − (7 # ( + (7 # +

# ( + 192

5. # + 4

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4

c.  = ; # ( − 44( (7

4: ;

#+3...