Column 1
How do you know if an equation is quadratic
A. If it has an exponent of 4
B. If it has no exponent
C. If it has 3 terms
D. If it has an exponent of 2
D. If it has an exponent of 2
Illuatrating quadratic equations:
One less than a number
answer: x-1
Solving QE by factoring
(8x+5)(4x-3)=0
Answer:
x= -5/8 | x= 3/4
completing the square
x2-10x-11
x=-1
x=11
Find the discriminant:
2x2 - 5x - 3 = 0
D=49
If an equation has a degree higher than 2 is it still quadratic?
No
Illustrating quadratic equations
2 more than 3 times a number
3x+2
Solving QE by factoring
(6x-3)(10x+9)=0
Answer: x= 3/6 or 1/2 | x= -9/10
completing the square
2x2-16x-10
x=8.58
x=-0.58
Find the discriminant:
2x2-4x-4=0
D=48
Which one of these is not quadratic
A. 2x^2 + 4x - 16 = 0
B. 8x^4 + 16x + 32 = 0
B.
Illustrating quadratic equation:
Suppose the length is 6 more than the width and the area is 475 cm.
what is the representation and the quadratic equation
representation:
quadratic equation:
representaion= Let x be the width
x+6= Length
Quadratic Equation: X2+6x-475=0
Solving QE by factoring
(2x+9)^2=0
x=-9/2
completing the square
3x2+18x-27
x=3
x=-9
Find the discriminant:
5x2+9x-20=0
D=481
Is 2x^2 - 3x = 0 quadratic
Yes even though it has only two terms it still has a degree of 2
Illustrating quadratic equation:
The length is 13 less than 2 times its width and the area is 475
Whats the representation and the quadratic formula
representation:
quadratic formula:
Representation: Let x be width
2x-13= Length
Quadratic equation: 2x2-13x-475=0
Solving QE by factoring
x2+7x+12=0
x= -4
x2=-3
completing the square
x2+4-10
x=-0.54
x=-7.46
Extracting roots
X²=4
answer: x=2 or x=-2
Find what makes the equation a non-quadratic and change it to make the equation quadratic
4x^4 + 16x + 256 = 0
Change the exponent of the first term to 2
Illustrating quadratic equations
The width is 1 more than its base and the area is 15
Find the representation and the quadratic equation
Representation:
Quadratic Equation:
Representation: Let x be the base
x+1=height
Quadratic equation: x2+x-30=0
Solving QE by factoring
2x2-11x+10=0
x= 10/2 or 5
x2= 1
completing the square
4x2+24x-28
x=3.08
x=-9.08
Extracting roots
3x²=12
answer: x=2