Vocabulary
A function can be written in ax^2+bx+c=0, where a, b, and c are real numbers and a ≠ 0.
What is the first step when it comes to using the quadratic formula?
Making sure that the quadratic equation is in standard form.
Identify a, b, and c:
-15x^2+8x=-5
a=-15, b=8, c=5
Solve the following quadratic equation by using the quadratic formula:
x^2+6x+19=10+6x
x = 3i, x = -3i
Find the discriminant & state the type of solutions.
8x-15=x^2
4
2 real (rational) solutions
What do they mean when they ask for the roots of the equation?
To give them all possible solutions to the equation, including even those that have imaginary numbers.
What is the second step of the quadratic formula?
Identifying a, b, and c from the quadratic equation.
Identify a, b, and c:
20x^2-9x=6
a=20, b=-9, c=-6
Solve the following quadratic equation by using the quadratic formula:
x(x-9)=-20
x = 5, x = 4
Find the discriminant & state the type of solutions.
x^2+25=10x
0
1 real (rataional) solution
What is the quadratic formula?
x=(-b±√(b²-4ac))/(2a)
When solving for the discriminant do you also have to take the square root?
No, you just use what's INSIDE the square root.
Identify a, b, and c:
-12x^2-9x-3=5
a=-12, b=-9, c=-8
Solve the following quadratic equation by using the quadratic formula:
3x^2+9x+3=2x^2-1
x = -1/2, x = -4
Find the discriminant & state the type of solutions.
5x^2=2x+2
44
2 real (irrational) solutions
Can a=0?
No, because on the quadratic formula the solution will be undefined. Also, this would be a linear function instead.
How many solutions can we get from the quadratic formula?
At most 2 solutions (using real or imaginary numbers).
Identify a, b, and c:
-13x^2-6x=-1+10x
a=-13, b=-16, c=1
Solve the following quadratic equation by using the quadratic formula:
4x^2=17x+15
x = 5, x = -3/4
Find the discriminant & state the type of solutions.
-x^2-4x=0
16
2 real (rational) solutions
Where is the discriminant found in the quadratic formula?
It is found under the radical: b^2-4ac. It does not include the radical.
In an application using projectile motion, how do you interpret the height if something hits the ground?
Ground level is a height of zero. So replace h = 0 into the equation and solve (only using the positive time value).
Identify a, b, and c:
32x^2+x=2x^2+10x+8
a=30, b=9, c=-8
or
a=-30, b=-9, c=8
Solve the following quadratic equation by using the quadratic formula:
5x^2+15=30x
3 pm (sqrt(6))
Find the discriminant & state the type of solutions.
4x^2+3=x(4-x)
-44
0 real solutions
2 imaginary numbers