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
x^2+8x+12=0
x=-4, -6
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
x2 + 4x = 0
x = 0, -4
What is the vertex of y = 2x2 - 5
(0, -5)
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.
0 = x2 - 8x +16
x = -4
x = -4
5x2+1=126
+5
-5
Find the vertex of f(x) = x2 + 2x +1
vertex (-1 0)
Solve the equation using the quadratic formula:
0 = x2 + 9x + 20
x = -5
x = -4
What is the discriminant of the following equations:
y=2x2+3x-10
89
Solve using the quadratic formula.
x2 + 6x + 2 = 0
x = 3 - sqrt(7) ,3+sqrt(7)
3x2 + 5x = 2x
x = 0, -1
What is the maximum or minimum value of
f(x) = 5 - 4x - x2
The maximum value is 9
Solve using the quadratic formula:
0 = 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
Where is the axis of symmetry of a function that has a y-intercept in -12 and zeros in -2 and 6?
x = 2