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
Which form of a quadratic function (most easily) gives the x-intercepts?
Factored form
x^2+8x+12=0
x=-4, -6
What is the vertex form of a quadratic function?
y = a(x-h)^2+k
What does the quadratic formula find?
zeros, x-intercepts, solutions or roots
If the discriminant is -900, how many solutions are there?
2 imaginary solutions.
Which method can be used to solve any quadratic equation?
Quadratic formula
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
Which form of a quadratic function (most easily) gives the y-intercept?
Standard Form
5x2+1=126
x= +5, -5
Find the vertex of f(x) = (x + 1)2
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
Which form of a quadratic function (most easily) gives the vertex?
Vertex Form
3x2 + 5x = 2x
x = 0, -1
Find the vertex of y = -3(x - 1)2 - 9
(1, -9)
Solve using the quadratic formula:
0 = -x2 + 14x - 49
x = 7
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
No real roots
Solve: 3x2 - 192 = 0
x= 8 , -8
Where is the axis of symmetry of the function: y = 12(x + 5)2 - 8?
x = -5