Quadratic Formula and Discriminant
Sing the quadratic formula song!
The opposite of B,
plus or minus the square root,
of B squared minus 4AC all over 2 times A !
Factor y=x2+8x + 16 to get the x-intercepts AND display the equation in factored form. Hint: (x+?)(x+?)
Factored form: (x+4)2 OR (x+4)(x+4)
The only solution is x = -4.
For what types of equations do you use the square root method ?
Binomial Quadratics !
What is the X-intercept of x2 ?
(0,0) !
Convert y = x2 + 6x + 9 to vertex form.
y = (x+3)2 !
How many X-intercepts does
y=2x2+ 3x - 2 have ? (Hint: Use the discriminant!)
2 !
Factor y=x2-x-6 to get the zeros AND display the equation in factored form. Hint: (x+?)(x+?)
The zeros are x = -2, 3
The factored form is: (x+2)(x-3)
Find the x-intercept(s) of
y = x2-9.
x = 3 !
Identify the vertex of:
-2(x + 3)2-4
(-3, -4) !
Convert y = x2-4x-5 to vertex form and find the x-intercepts.
Vertex form: y = (x-2)2-9
X-Intercepts: x = -1, 5
Use the quadratic formula to identify the solutions of
y= -x2+2x+3
x = -1, 3 !
Factor y=x2-3x-28 to get the zeros AND display the equation in factored form. Hint: (x+?)(x+?)
The zeros are x = -4, 7
The factored form is: (x-7)(x+4)
Find the x-intercepts of y = x2 + 9 !
x = ± 3i !
Convert -2(x + 3)2-4 into standard form !
3x2+18x+23 !
Convert y = x2+2x-8 to vertex form and find the x-intercepts !
Vertex form: y = (x+1)2-9
X-Intercepts: x = 2, -4
How many X-intercepts does y=x2 + 6x+9 have ?
1 !
Factor y=3x2-x-2 to get the zeros AND display the equation in factored form.
Factored form: (3x+2)(x-1)
The zeros are x= 1, -2/3!
Find the x-intercepts of y=-5x2 +125.
x = ± 5 !
What is the Y-Intercept of 1205x2 + 104x + 2
2 !
Convert y=-x2 +10x + 2 to vertex form !
y = -(x-5)2+27
Use the quadratic fomula to solve for the solutions of y=-2x2-2x + 1 !
(-1 ±√3)/2
Factor y=-2x2-3x-2 to get the zeros AND display the equation in factored form.
Factored form: (-2x+1)(x+2)
The zeros are x = -2, 1/2
Find the x-intercepts of
y = 5x2+25.
± √(5)i !
Write a vertex form equation that moves the graph of x2 3 units to the right, 2 units down, makes it wider, and flips it across the x-axis.
Varies
Convert y = 3x2 + 18x + 4 to vertex form and find the x-intercepts.
Vertex form: y = 3(x+3)2-23.
x-intercepts: -3 ± √(23/3)