Vocabulary
What is the standard form of a quadratic function?
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+5=0
x = -1, x = -5
Find the discriminant & state the type of solutions.
-x^2+8x-15=0
4
2 real solutions
What is the quadratic formula?
x=(-b±√(b²-4ac))/(2a)
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^2-9x+20=0
x = 5, x = 4
Find the discriminant & state the type of solutions.
x^2-2x+1=0
0
1 real solution
Where is the discriminant found in the quadratic formula?
under the square root
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:
2x^2+9x+4=0
x = -1/2, x = -4
Find the discriminant & state the type of solutions.
5x^2+2x-2=0
44
2 real solutions
What is the discriminant?
b^2-4ac
How many solutions can we get from the quadratic formula?
At most 2
Identify a, b, and c:
-13x^2-16x=-1
a=-13, b=-16, c=1
Solve the following quadratic equation by using the quadratic formula:
4x^2-17x-15=0
x = 5, x = -3/4
Find the discriminant & state the type of solutions.
-x^2-4x=0
16
2 real solutions
Can a=0?
No, because on the quadratic formula the solution will be undefined.
What do you always put when taking the square root of something?
Plus or minus
Identify a, b, and c:
30x^2=-9x+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^2-30x+15=0
3 pm (sqrt(6))
ind the discriminant & state the type of solutions.
5x^2+4x+3=0
44
0 real solutions
2 imaginary