Quadratic Formula
What is the quadratic formula?
x=(-b+-sqrt(b^2-4ac))/(2a)
If the discriminant is 15, how many solutions and what type are they?
2 real solutons
Write the coefficients of the equation (when in standard form):
11x^2-5x=-2
a=11, b=-5, c=2
Write the general form for a quadratic in standard form.
ax^2+bx+c=0
What does the quadratic formula find?
The zeros or x-intercepts
If the discriminant is -900, how many solutions are there?
2 imaginary solutions.
Solve using factoring.
2x2-18x+40=0
x = 4
x=5
2x2=8
+2
-2
Using the quadratic formula find the zeros:
y=x2-5x+6
x=3
x=2
What is the discriminant of the following equations:
y=x2+4x+6
discriminant = -8
Solve using factoring.
y = x2 - 8x +16
x = -4
x= -4
5x2+1=126
+5
-5
Solve the equations using the quadratic formula:
y=x2+9x+20
x=-5
x=-4
What is the discriminant of the following equations:
y=2x2+3x-10
89
Solve using completing the square.
x2 + 6x + 2 = 0
x = 3 - sqrt(7) ,3+sqrt(7)
Is the discriminant in the quadratic formula?
Yes
Solve using the quadratic formula:
y=x2+7x+20
(-7+-sqrt(31)i)/2
What does the discriminant tell you?
The number and type of solutions that a quadratic has.
Solve using whatever method you think is most appropriate.
3x2-4x+4 =0
𝑥=2/3 ± (2√2𝑖)/3
Solve: x2 +25=0
x= 5i , -5i