VCE Methods Quadratic Review

Solve the quadratic by factoring

100

(x+5)(x-1)=0

x= -5

x=1

200

(2m+3)(4m+3)=0

m= -3/2

m= -3/4

300

n²+7n+10=0

(n+5)(n+2) so...

n= -5

n= -2

400

7r²-14r=-7

7r²-14r+7=0 (divide everything by 7)

7(r²-2r+1)=0

7(r-1)(r-1)=0 so ...

r= 1

500

2x²+7x-4=0

Have to do factor by grouping...

2(-4)=-8

Multiply to get -8, add to get 7

So 8 and -1

2x²+8x     -1x-4

2x(x+4)   -1(x+4)

(2x-1)(x+4)=0 so...

x= 1/2

x= -4

Turning Point Form

100

Find the vertex of the following parabola.

y = (x-3)²-4

V= (3,-4)

200

Find the axis of symmetry of the following parabola.

y = (x+1/2)²+3

x = -1/2

300

Put the following in turning point form.

y= x²-4x

y=(x-2)²-4

400

Solve the equation by completing the square. 

n²-2n=3

n=3

n=-1

500

Find the vertex of the following. 

y=2x²-2x-5

V = (1/2, -11/6)

Solve the quadratics using square roots

100

Solve each equation by taking square roots. 

k²=16

k= 4, -4

200

Solve each equation by taking square roots. 

2n²=-144

no solution! Can't take the square root of a negative!

300

Solve each equation by taking square roots. 

m²+7=88

m= 9, -9

400

Solve each equation by taking square roots. 

2(x+4)²=10

x= -4 +/- square root of 4

500

Solve each equation by taking square roots. 

(3x+1)² - 36=0

x= 5/3, x= -7/3

Find the discriminant

100

Find the discriminant of each quadratic equation then state the number of real and imaginary solutions. 

6p²-2p-3=0

Discriminant: 76

2 real solutions

200

Find the discriminant of each quadratic equation then state the number of real and imaginary solutions. 

-2x²-x-1=0

Discriminant: -7

2 imaginary solutions

300

Find the discriminant of each quadratic equation then state the number of real and imaginary solutions. 

-2x²-8x-8=0

Discriminant: 0

One real solution

400

Find the discriminant of each quadratic equation then state the number of real and imaginary solutions. 

9m²+6m+6=5

Discriminant: 0

One real solution

500

Find the discriminant of each quadratic equation then state the number of real and imaginary solutions. 

-9b²= -8b+8

Discriminant: -224

2 imaginary solutions

Quadratic Formula

100

Solve using the quadratic formula:

m²-5m-14=0

m= 7

m= -2

200

Use the quadratic formula to solve the equation:

b²-4b+4 =0

b= 2

300

Use the quadratic formula to solve the equation:

2x²+3x-20= 0

x= 5/2

x= -4

400

Use the quadratic formula to solve the equation:

4b²+8b+7=4

*remember it should equal 0 before you start!*

b= -1/2

b= -3/2

500

Use the quadratic formula to solve the equation:

2x²-3x-15= 5

x= 4

x= -5/2