3.1 Writing Quadratic Equations

Multiple Choice

What form of a quadratic is given?

$$f\left(x\right)=2x^2+3x-4$$  

• Vertex Form

• Standard Form

• Root Form

3.1 Writing Quadratic Equations

Have your notebook nearby to show your work!

Forms of Quadratic Functions

Multiple Choice

What form of a quadratic is given?

$$f\left(x\right)=3\left(x-2\right)^2+4$$  

• Vertex Form

• Standard Form

• Root Form

Multiple Choice

What form of a quadratic is given?

$$f\left(x\right)=-\left(x+2\right)\left(x-5\right)$$  

• Vertex Form

• Standard Form

• Root Form

Multiple Choice

Find the equation for a parabola that has a vertex at (3, 4) and goes through the point (2, 2).

• $$y=\left(x-3\right)^2+4$$

• $$y=-\frac{2}{25}\left(x+3\right)^2+4$$

• $$y=-2\left(x-3\right)^2+4$$

• $$y=-2\left(x+3\right)^2-4$$

Guide number
14
1x14
2x7

Solving

q

uadratic

e

quations

x

squared,

x

’s, number equals zero

2

SOLVE

5

14

0

x

x−

−

=

Can we FACTORISE ?

(

)(

)

0

x

x

=

Subtract to 13
No Good
Subtract to 5
Yes! Perfect

-

(

)

(

)

+ 2

0

7

0

2

7

=

−

=

= −

=

x

x

x

x

Factorised

Solved

(

2)(

7)

0

x

x

+

−

=

08:02

Multiple Choice

Lets do another problem just to make sure we've got this.

Find the equation of a parabola that has a vertex at (2, -7) and goes through the point (3, -4).

• $$y=\frac{3}{25}\left(x+2\right)^2-7$$

• $$y=3\left(x-2\right)^2-7$$

• $$y=3\left(x+2\right)^2-7$$

• $$y=\left(x-2\right)^2-7$$

Fill in the Blank

Given the equation

$$f\left(x\right)=-5\left(x-2\right)^2-4$$ , what is the vertex for the parabola? 
Write your answer as a coordinate point. (x, y)

Section A
Section B
Section C
Section D
Section E
Section F
Index
Section G

𝑥2– 5𝑥 + 6

Factoring 𝑥2+ 𝑏𝑥 + 𝑐

•Multiply coefficient of 𝑥2 and the constant to get the guide number

•Find the factor pairs of this number

•We want the factor pair that sums to give the middle term

•Split the middle term up using these two terms

•Factorise the four terms by grouping

08:02

𝑥2– 5𝑥 + 6

𝒙𝟐− 𝟑𝒙 − 𝟐𝒙 + 𝟔

𝑥2– 5𝑥 + 6

𝒙𝟐− 𝟑𝒙 − 𝟐𝒙 + 𝟔

𝒙(𝒙 − 𝟑) − 𝟐(𝒙 − 𝟑)

𝑥2– 5𝑥 + 6

𝒙𝟐− 𝟑𝒙 − 𝟐𝒙 + 𝟔

𝒙(𝒙 − 𝟑) − 𝟐(𝒙 − 𝟑)

(𝒙 − 𝟑)(𝒙 − 𝟐)

𝟏 𝒙 𝟔

− 𝟏 𝒙 − 𝟔

𝟐 𝒙 𝟑

− 𝟐 𝒙 − 𝟑

+6

Section A
Section B
Section C
Section D
Section E
Section F
Index
Section G

x

x

− 3

x2

− 3x

− 2x

+6

•Multiply coefficient of 𝑥2 and the

constant to get the guide number

•Find the factor pairs of this number

•We want the factor pair that sums to

give the middle term

•Split the middle term up using these

two terms

•Factorise the four terms by grouping

08:02

− 2

𝑥2– 5𝑥 + 6𝑥2– 5𝑥 + 6

𝒙𝟐− 𝟑𝒙 − 𝟐𝒙 + 𝟔

𝑥2– 5𝑥 + 6

𝒙𝟐− 𝟑𝒙 − 𝟐𝒙 + 𝟔

(𝒙 − 𝟑)(𝒙 − 𝟐)

𝟏 𝒙 𝟔

− 𝟏 𝒙 − 𝟔

𝟐 𝒙 𝟑

− 𝟐 𝒙 − 𝟑

+6

Factoring 𝑥2+ 𝑏𝑥 + 𝑐

Multiple Select

Given the equation

$$f\left(x\right)=2\left(x-4\right)\left(x+6\right)$$ , determine the roots (zeros) for this parabola.

Select all that apply.

• x = -6

• x = -4

• x = 2

• x = 4

• x = 6